This is not to say I don't agree that I doubt the witnesses or that at least one missile was involved.
To the extent that many independent witnesses report seeing a magician pull a rabbit out of a hat tends to refute a hypothesis that there is not one scintilla of evidence of a rabbit. True, they might not be able to put together the entire, correct, detailed scenario of how the magician did it. But should the NTSB (National Tricks and Subterfuge Bureau) categorically state the "card trick theory" is favored and that was no evidence of a rabbit at any time, and that therefore the witnesses must have been drunk, you may reasonably suspect that something is up.
This would appear to be the case with the missile theory and TWA 800 - except that there are also the matters of Mach 2 debris exiting the plane just before breakup, and the red residue and misrepresentation in court about it, and a secret evidence room for the FBI, and shrapnel removed from the victims, and some mysterious, fleeting radar hits prior to breakup, and the nose gear doors being blown inward and being among the first things off the plane, and fist-sized holes in some first-class seat-backs ... and the fact that aviation fuel puts out matches, and so on.