Well... it was a JOINT NATION EXERCISE. They were testing a new anti-aircraft/anti-missile missile. There may have been several different versions of this missile being testing by the UK or the French. The missile was designed not to HIT the TARGET, but to detonate when near. One of the release charges was metal pellets, and another was a razor sharp tungsten ring that enlarged radially outward, cutting anything nearby in half.
They were shooting at a a towed Target Drone, IIRC, and TWA800 got a little too close to the 'area' and the missile found a bigger 'signature' and followed it.
Which 'ship' launched the missile and which nation that ship belong to, is what has been kept secret. So far.
It was a big dog and pony show conducted in an uncontrollable airspace (they were purposely conducting the test in waters near the airport as proof of how well this new missile would work), and Murphy's Law triumphed.
It was decided, at the highest levels, that for the good of all the nations involved in the test, that the truth would be kept hidden and would be classified as a matter of 'national security' and the men on all those ships were sworn to secrecy under penalty of death, before the next day dawned.
So hundreds of crewmen who were part of the exercise never talked? Never told their wives, husbands, family members, friends, anyone? No one made an anonymous call? Ridiculous.