IIRC part of the story was the Prime Minister of Israel was on an EL AL 747 scheduled to depart JFK ahead of TWA 800. For some reason they pulled into a holding pad , and TWA 800 took off before them. That lends some credence to the advisory shot down from a manpad in a small boat that sped away after the shoot down.
If the US Navy errantly shot TWA down with a missile durning an exercise...that would be almost impossible to cover up with so many people involved.
How many people on a Navy ship would have known if they had shot down TWA 800?