“There was a rumor that it was a US sub that shot down the TWA 800. “
And what US subs carry anti-air missiles?
Er, The Soviet Kilo class submarine had anti aircraft missiles since 1982.
I don’t know if it is fielded yet, but in fact subs can now launch AA missiles, though generally not to the altitude of TWA800:
https://en.wikipedia.org/wiki/IDAS_(missile)
The US system is more advanced, though I vaguely recall it is ejected out of somewhere extremely unlikely, like the garbage ejector.