I've run into the claim that in the U.S. that treason must be tried by a military tribunal, even if the accused is a civilian. Is this true? I tried Googling the question, but it seems I don't know enough about the law to be able to find the answer that way.
It is not the case that treason must be tried by a military tribunal. See for example US v. Kawakita, which was an ordinary civilian jury trial. I cannot even imagine why one would think that there is any such requirement. Here is the federal law against treason, and nothing says "offenses must be tried in a military court". Perhaps that misconception was based on the use of military tribunals during the American Revolution, which preceded the creation of a US legal system.
Actually, the opposite is true: a military tribunal cannot try a treason case. A military tribunal can only handle cases arising from the Uniform Code of Military Justice or other laws that state that they can be tried by a military tribunal.
Military Tribunals have a specific legal definition and are not typically a thing in the U.S. (they can only be used if regular courts are not functioning). You may be thinking of a Court Marshal, which is a trial of a member of a military service for a crime committed under the jurisdiction of the Uniform Code of Military Justice. They function like a typical U.S. civilian court, with the exception that the jury must be members of the military (and a certain subset must be enlisted personnel if the accused is enlisted and may not be of a lower rank than the accused).
Treason is a specific crime in the United States and while persons accused of Treason can be military, they need not be. John Brown, the first person accused of and executed for treason (against the Commonwealth of Virginia) in the U.S. was a civilian abolitionist who was trying to provoke a slave rebellion and was not prosecuted in any court under Military Jurisdiction. Treason is uniquely the only law listed in the Constitution that a person who is not an agent of the government can break (kinda ... the U.S. Constitution limits what "Treason" is and lists the standards of evidence). That said, certain actions that may be treasonous are not legally treason for the evidence reasons (All accusations of treason must have two witnesses for each action, which is a high threshold for a single treasonous act). Crimes of a similar nature are not so difficult to prove: e.g., Espionage is a separate crime to treason and does not meet the standards... however it could be treasonous too.
In the entire history of the United States, there has been less than 30 cases of people charged with treason (state or federal), 14 of which were state treason charges, of which only six were convicted and only 5 of those convicted were executed. Federally, only one person has been executed for treason William Bruce Mumford (who was tried by a military tribunal in Union occupied New Orleans in 1862). At the time, he was not in military service (union or confederacy). His crime was tearing down the U.S. flag in an act of support for the Confederacy.
Actually, thats wrong. There is a distinction between a military tribunal and a court martial. A military tribunal is designed to prosecute enemy combatants under the laws of armed conflict during wartime. Civilians can be detained indefinently at Guantanamo, since after 9/11, by order of George W. Bush. American citizens who collaborate with the enemy during wartime are considered enemy combatants and are treated differently.
Courts martial on the other hand, address only those who are subject to the UCMJ, such as American members of the armed forces.
There are times when the military can/must try someone for treason in a tribunal. When a war has been declared (there doesn't have to be fighting going on), acts of treason fall under the UCMJ and the military can use a tribunal. However, if there isn't a functioning government (say President election was proven fraud invalidating all appointees), then military must handle prosecutions for treason that led to such fraud.