They are not random, that's the point. They're entirely deterministic and very precise, and they aren't hiding anything; they will give you the most likely (not blacklisted) sequence of characters to follow your input according to their model. What they won't give you is information, except by accident.
If they were random (hidden or not) they'd be harmless, no one would trust them any more than one of those eight ball toys, or your average horoscope.
The issue is that they're very not random, so much that there's no way to know if what they are saying bears any accidental semblance to the truth without fact checking... and that very soon they'll have replaced any feasible way to fact check them, since all the supposed "facts" we'll have access to will have been generated by LLMs train on LLM generated garbage.