Having a mathematical proof is nice, but honestly this whole misunderstanding could have been avoided if we'd just picked a different name for the concept of "producing false information in the course of generating probabilistic text".
"Hallucination" makes it sound like something is going awry in the normal functioning of the model, which subtly suggests that if we could just identify what went awry we could get rid of the problem and restore normal cognitive function to the LLM. The trouble is that the normal functioning of the model is simply to produce plausible-sounding text.
A "hallucination" is not a malfunction of the model, it's a value judgement we assign to the resulting text. All it says is that the text produced is not fit for purpose. Seen through that lens it's obvious that mitigating hallucinations and creating "alignment" are actually identical problems, and we won't solve one without the other.