Is this really a valid characterization of the decision, or hyperbole
to express her distaste for the majority opinion?
Short Answer
It is a valid characterization.
Long Answer
The legal standard under the Trump v. U.S.
The U.S. Supreme Court majority opinion specifically discusses the fact that the commander-in-chief power and the pardon power are among the core powers of the President for which it later opines that he has absolute immunity from criminal liability. I'll quote that at length (paragraph breaks inserted potentially differently from the original for readability in this format, emphasis mine) at pages 6-9 of the Slip Opinion linked in the question:
Article II of the Constitution provides that “[t]he executive Power
shall be vested in a President of the United States of America.” §1,
cl. 1.
The President’s duties are of “unrivaled gravity and breadth.” Trump
v. Vance, 591 U. S. 786, 800 (2020). They include, for instance,
commanding the Armed Forces of the United States; granting reprieves
and pardons for offenses against the United States; and appointing
public ministers and consuls, the Justices of this Court, and Officers
of the United States. See §2. He also has important foreign
relations responsibilities: making treaties, appointing ambassadors,
recognizing foreign governments, meeting foreign leaders, overseeing
international diplomacy and intelligence gathering, and managing
matters related to terrorism, trade, and immigration. See §§2, 3.
Domestically, he must “take Care that the Laws be faithfully
executed,” §3, and he bears responsibility for the actions of the many
departments and agencies within the Executive Branch. He also plays a
role in lawmaking by recommending to Congress the measures he thinks
wise and signing or vetoing the bills Congress passes. See Art. I,
§7, cl. 2; Art. II, §3.
No matter the context, the President’s authority to act necessarily
“stem[s] either from an act of Congress or from the Constitution
itself.” Youngstown, 343 U. S., at 585. In the latter case, the
President’s authority is sometimes “conclusive and preclusive.” Id.,
at 638 (Jackson, J., concurring). When the President exercises such
authority, he may act even when the measures he takes are
“incompatible with the expressed or implied will of Congress.” Id.,
at 637. The exclusive constitutional authority of the President
“disabl[es] the Congress from acting upon the subject.” Id., at
637–638. And the courts have “no power to control [the President’s]
discretion” when he acts pursuant to the powers invested exclusively
in him by the Constitution. Marbury, 1 Cranch, at 166. If the
President claims authority to act but in fact exercises mere
“individual will” and “authority without law,” the courts may say so.
Youngstown, 343 U. S., at 655 (Jackson, J., concurring).
In Youngstown, for instance, we held that President Truman exceeded
his constitutional authority when he seized most of the Nation’s steel
mills. See id., at 582–589 (majority opinion). But once it is
determined that the President acted within the scope of his exclusive
authority, his discretion in exercising such authority cannot be
subject to further judicial examination.
The Constitution, for example, vests the “Power to Grant Reprieves and
Pardons for Offences against the United States” in the President. Art.
II, §2, cl. 1. During and after the Civil War, President Lincoln
offered a full pardon, with restoration of property rights, to anyone
who had “engaged in the rebellion” but agreed to take an oath of
allegiance to the Union. United States v. Klein, 13 Wall. 128,
139–141 (1872). But in 1870, Congress enacted a provision that
prohibited using the President’s pardon as evidence of restoration of
property rights. Id., at 143–144. Chief Justice Chase held the
provision unconstitutional because it “impair[ed] the effect of a
pardon, and thus infring[ed] the constitutional power of the
Executive.” Id., at 147. “To the executive alone is intrusted the
power of pardon,” and the “legislature cannot change the effect of
such a pardon any more than the executive can change a law.” Id., at
147–148. The President’s authority to pardon, in other words, is
“conclusive and preclusive,” “disabling the Congress from acting upon
the subject.” Youngstown, 343 U. S., at 637–638 (Jackson, J.,
concurring).
Some of the President’s other constitutional powers also fit that
description. “The President’s power to remove—and thus
supervise—those who wield executive power on his behalf,” for
instance, “follows from the text of Article II.” Seila Law LLC v.
Consumer Financial Protection Bureau, 591 U. S. 197, 204 (2020). We
have thus held that Congress lacks authority to control the
President’s “unrestricted power of removal” with respect to “executive
officers of the United States whom he has appointed.” Myers v.
United States, 272 U. S. 52, 106, 176 (1926); see Youngstown, 343
U. S., at 638, n. 4 (Jackson, J., concurring) (citing the President’s
“exclusive power of removal in executive agencies” as an example of
“conclusive and preclusive” constitutional authority); cf. Seila
Law, 591 U. S., at 215 (noting only “two exceptions to the
President’s unrestricted removal power”).
The power “to control recognition determinations” of foreign countries
is likewise an “exclusive power of the President.” Zivotofsky v.
Kerry, 576 U. S. 1, 32 (2015). Congressional commands contrary to
the President’s recognition determinations are thus invalid. Ibid.
Congress cannot act on, and courts cannot examine, the President’s
actions on subjects within his “conclusive and preclusive”
constitutional authority.
It follows that an Act of Congress—either a specific one targeted at
the President or a generally applicable one—may not criminalize the
President’s actions within his exclusive constitutional power. Neither
may the courts adjudicate a criminal prosecution that examines such
Presidential actions. We thus conclude that the President is
absolutely immune from criminal prosecution for conduct within his
exclusive sphere of constitutional authority.
Individual Examples Considered
Orders the Navy’s Seal Team 6 to assassinate a political rival?
When the U.S. President as commander-in-chief of the U.S. military directs the U.S. military to take a particular military action, this is an act involving the core official duties of the U.S. President.
In contrast, for example, if the President murders his wife in a domestic dispute in a White House bedroom, which would be a private act of the President, which would not plausibly implicate any of his official acts or duties, he would not have criminal immunity.
The power to direct members of the U.S. military as commander-in-chief is a core duty of the President whether the acts take place at home or abroad, and whether they are carried out with or without a Congressional authorization to use military force. The Commander-in-Chief power applies just as much to soldiers stationed at Leavenworth or Fort Carson as it does to a soldier deployed in Afghanistan while U.S. forces were engaged in combat there.
Congress clearly does not have the power to take away the President's role as commander-in-chief of the U.S. military, so acts of the President conducted in that role would almost surely be "core" official acts of the President.
The fact that this is clearly an unlawful order and a crime is irrelevant, because the President has absolute immunity for core official acts of the President. All immunity cases involve an official act that is nonetheless a crime. If that weren't the case, it wouldn't be an immunity from criminal liability at all.
If the soldiers who were ordered to kill a political rival actually did so, they would be carrying out a clearly illegal order and would have criminal liability and liability under the Uniform Code of Military Justice for doing so.
But, the President could pardon the soldiers who follows his orders, even before they were charged and before the President's term ended, at least from any federal crime or UCMJ charge.
Takes a bribe in exchange for a pardon?
The same analysis applies to taking a bribe in exchange for a pardon. Granting a pardon is a core official act of the President set forth in the constitution, and which the President is allowed to carry out in a plenary fashion without Congressional limitation or judicial review.
Indeed, the legality of cases where a President accepts campaign contributions that are a quid-pro-quo for a pardon, which Trump is known to have done, isn't even seriously questioned as things stand now. See, e.g., here.
So, if the bribery prosecution relies upon there being a quid-pro-quo of the benefit for the official act of granting a pardon, again, the President has absolute immunity.
Perhaps, if the receipt of benefit, an emolument (i.e. an economic benefit not authorized by Congress), is a crime, even without the quid-pro-quo, that lesser charge might be a case of mere presumptive immunity or a private act. Unlike the pardon power or the commander-in-chief power, the President is expressly prohibited by the U.S. Constitution from receiving emoluments, so receiving them is certainly not a core power of the President. But, it appears that no federal criminal statute punishes receipt of emoluments and it is unclear if anyone can have standing to enforce this requirement in a civil lawsuit. Trump himself beat multiple civil emoluments lawsuits, with help from SCOTUS, while he was President, and while President, he could decline to allow himself to prosecuted for this intrinsically federal offense.
But, this would no doubt be a significantly lesser charge than a bribery charge, even if it was a crime.
Of course, the person offering the bribe wouldn't have Presidential immunity. But, that person could also be pardoned by the President.
(I disagree with legal scholars who believe that the President can pardon himself, although this would be an issue of first impression as it has never been attempted at the federal level by any President to date and Nixon, at least, believed that he did not have that power. The majority's elaborate analysis of when the President does and does not have immunity from criminal charges would be virtually irrelevant if he did have the power to self-pardon.)
Organizes a military coup to hold onto power?
This is a little less definitive, because "organizes a military coup" isn't a single well-defined act, and instead it is a course of multiple actions over time. But to the extent that the underlying conduct described is commanding the military to take particular actions, the same analysis as the Seal Team 6 case applies.
This would probably be treason, as defined in the U.S. Constitution, but the U.S. Supreme Court didn't leave any room for a treason exception to absolute immunity from criminal liability for the core official acts of the President.
The Slip Opinion at pages 16-30 examines many of the acts alleged in the January 6 prosecution indictment and concludes that at least some of those acts, which if proven amount to steps that are part of an effort to organize a non-military coup, amount to official acts for which the President is immune from criminal liability. The space limitations of Law.SE answer makes it impossible to quote this analysis at length.
Near the conclusion of this analysis the majority opinion states on page 30 of the Slip Opinion:
The essence of immunity “is its possessor’s entitlement not to have to
answer for his conduct” in court. Mitchell, 472 U. S., at 525.
Presidents therefore cannot be indicted based on conduct for which
they are immune from prosecution. As we have explained, the indictment
here alleges at least some such conduct. See Part III–B–1, supra. On
remand, the District Court must carefully analyze the indictment’s
remaining allegations to determine whether they too involve conduct
for which a President must be immune from prosecution. And the parties
and the District Court must ensure that sufficient allegations support
the indictment’s charges without such conduct.
Observation
The absolute immunity ruling is also particularly problematic in light of the impeachment language of the U.S. Constitution, which contemplates that a government official, including the President, may be criminally prosecuted for conduct separately from an impeachment proceeding which merely removes someone from office, even if they overlap and involve official acts.
Article I, Section 3, Clause 7 of the U.S. Constitution states (emphasis added):
Judgment in Cases of Impeachment shall not extend further than to
removal from Office, and disqualification to hold and enjoy any Office
of honor, Trust or Profit under the United States: but the Party
convicted shall nevertheless be liable and subject to Indictment,
Trial, Judgment and Punishment, according to Law.
While this could be read as conditioning criminal charges arising from impeachable conduct on an impeachment conviction, no President has even been convicted in an impeachment proceeding, and the this clause of the U.S. Constitution has not been interpreted this way in the case of impeachments involving individuals other than the U.S. President. The majority opinion rejects this reading of this clause of the U.S. Constitution at pages 31-34 of the Slip Opinion.
Still, it is hard to reconcile the implications of this language with absolute Presidential immunity from criminal liability for core official acts of the President that the majority opinion concludes exists. The majority opinion does just this, however, directly engaging with and rejecting this argument at page 38 of the Slip Opinion.
Congressional Immunity Compared
It is also worth observing that the absolute and presumptive immunity that SCOTUS granted to the President in this case is broader than the immunity granted to members of Congress (who also have absolute immunity from civil liability for their legislative acts), under the Speech and Debate Clause of the U.S. Constitution, which contains some exceptions. The clause states that:
The Senators and Representatives shall in all Cases, except Treason,
Felony, and Breach of the Peace, be privileged from Arrest during
their attendance at the Session of their Respective Houses, and in
going to and from the same; and for any Speech or Debate in either
House, they shall not be questioned in any other Place.
The Speech and Debate Clause retains criminal liability for treason and felonies, even when committed in the course of a Senator or Representative's official duties, and even criminal liability for misdemeanors in cases that involve a breach of the peace.
Absolute immunity and presumptive immunity of the President for his or her official acts, in contrast, contains no such exceptions.
Can we really know one way or the other if these examples are accurate?
Is it even possible to determine this from the opinion, or must we
wait until one of these hypothetical situations occurs and the court
has to decide it?
Applying a legal precedent to a new set of facts is always a mix of art and science.
But, the majority opinion provides considerable and detailed guidance to evaluate these scenarios as described above. It is possible to apply the majority opinion to a set of facts about which the majority opinion discusses relevant legal considerations and make a well-informed judgment. We can't know for sure until one of these situations comes up and is decided, but we can have quite high levels of confidence about what this decision implies in this particular examples.
The majority opinion states at page 37 of the Slip Opinion that:
As for the dissents, they strike a tone of chilling doom that is
wholly disproportionate to what the Court actually does today[.]
When the majority opinion says this, it is being clearly and brazenly dishonest.