Hmmm ... On the surface its a silly question, designed to get impassioned responses and fan flames but you lay out some well reasoned thoughts. Lets frame it this way:
someone comes to you and claims to be gods sole representative. They claim that if you dont accept what they say as comming from god himself then god himself will kill you, and soon, when he kills the resf of the world.
Yes. They are certifiably bat poop crazy. They are functioning, they can pass as mentally stable, but their delusion is deep.