Yes you are, regarding LLMs at least. Here's why:
just for fun I asked a reasonably smart LLM to ...
[be] capable of understanding if it's gone off on
a hallucinatory path ...
"Smart" in this context is a subjective value judgement.
"Hallucinations" are only experienced by living organisms.You then went on to state:
> If you know something rare and the LLM does not, you'll immediately see when it's hallucinating an answer or answering factually.
Again, "hallucinating" is not something an algorithm can do. Also, determining factuality is again subjective based on the person assessing the information.