Consider the burden of proof.
It doesn't even matter that NASA did or didn't disprove the doomsday claims (but if there's anywhere I can read them, I'd like to). I don't think it is possible to disprove the claims. It depends on how vague they are, of course. If they just say "the world will end on that date", that's very vague, and there could be some things which can wipe out humanity (nuclear war, large celestial object we somehow didn't see, etc.).
The point is just that there is absolutely no reason to believe it when they don't come up with evidence or even good logic for their claims. Then it can be thrown into the same dustbin of fiction as fairies, witches, gods, smurfs, etc.