Edit:
To answer why the intent of the speaker, I'd like to use my go favorite lawyer movie, "My Cousin Vinny" to show how context when related to speech is very critical.
The cousin of Vinny (Bill) is from Brooklyn and is charged with a murder of a shop clerk he did not commit in rural Alabama (The viewer knows this). The cousin believes that he was arrested for an honest mistake petty theft of a can of tuna from the same store (he was probably the last person to see the clerk alive). When he tries to confess to taking the tuna, the sheriff believes he was confessing to the murder of the clerk, and when the sheriff gets impatient, we get to this exchange:
Sheriff: When did you shoot him?
Bill: what?
Sheriff: At what point did you shoot the clerk?
Bill (confused): I shot the clerk?
Sheriff: Yes, when did you shoot him?
Bill (still processing the question): I shot the clerk?!
Officer: Dean, we need you out here!
Sheriff: I'm right in the middle of a damn confession here! (Sheriff
and Deputy leave room. Bill realizes...)
Bill: WHOA!!! Wait a minute!!
It's important to state that there is no malicious on this part. My Cousin Vinny was praised for it's ability to show that the witnesses for the prosecution were not corrupt country hicks that sleep with their sisters, as the movie puts it in more crass language. The sheriff does actually help Vinny win the case at a point where he makes it clear that it is not part of his job and once new evidence comes to light the prosecution does admit it got it wrong (he's even given a sympathetic story to show he's not a bad guy). In the above scene, Bill is clearly trying to work through what the sheriff asked him and is quite floored by the accusation that is made. The sheriff believes he's confessing to the murder, not petty theft and thinks Bill is stalling, and both are unfamiliar with each others accents. Furthering the problem an officer pulls the sheriff away as Bill comes to the realization of the gravity of the situation he's in but the Sheriff is distracted by other matters and doesn't catch these changes in attitude going on. And later in this movie, the fruits of this scene come to bear when the sheriff is testifying in court
Sheriff: (dryly without any hint of emotion) I asked him if he did it, and he said 'I shot the clerk.' I asked him again, and again he said 'I shot the clerk.'
The sheriff, in complete earnest, has turned Bill's questions made in a state of utter confusion to be statements of fact. An emotionless quotation of an utterance is quite plausible in court. Even if the sheriff was personally out to get Bill, he's been in court enough times to testify to all manner of crimes that he has developed a dry read of statements because he's relying on the facts and facts alone.
This scene is usually used to show what they mean by "Anything you say can and will be used against you" during Miranda reads. In fact, because of rules on Hearsay, an arresting officer can only testify to statements you made that are injurious to you... if you say over and over that You are Innocent, he cannot attest to those statements during trial.
But we can also use it to show why context and intent of speech is important. In this case, the difference in punctuation of the spoken words "I shot the clerk?!" and "I shot the Clerk." are so vast that in the court of law, it's the difference between innocence and guilt. And because punctuation is not heard in an English statement, things such as tone are used to convey the question. You probably even read the two quoted statements in completely different tones, even though they were side by side.
Again, it's important to know that the sheriff did not deliberately misrepresent Bill's statement. He gave an accurate report of the statement as he recalled it. The analysis of the error was not really explored because the charge was for murder, not a true threat, so free speech issues weren't discussed much in that issue. However, had this been a free speech error, the misread is a critical mistake that could have flipped the case against Bill despite the fact that Bill never would have confessed had he known ahead of time that he was under arrest for murder. Here, it only put him up for the death penalty.
And as a final note, I did leave something out on Watts: He did in fact commit a crime that night. Watts was found in possession of marijuana during a search related to his arrest for making a threat against the President. He was found guilty of the crime well before his case was decided by the Supreme Court. When the court ruled in his favor, this case was overturned by lower courts because the cause for the search (the arrest for threatening the president) was no longer a valid arrest, and thus the probable cause for the search and the evidence was only found on that justification. Just to stress how absolutely critical a speaker's intended meaning is to a case of True Threat.