To make a clear example, is the fact that when prompting GPT-5 with "Solve 5.x = x + 5.11" it answers "-0.21" (making the same mistake as when it GPT-4 says 5.11 > 5.9). Is that example specifically in the training data? Who knows! But are those types of problems in the training data? Absolutely! So is this a mistake or a hallucination? Should we really be using an answer that requires knowing the exact details of the training data? That would be fruitless and allow any hallucination to be claimed as a mistake. But in distribution? Well that works because we can know the types of problems trained on. It is also much more useful given that the reason we build these machines is for generalization.
But even without that ambiguity I think it still gets difficult to differentiate a mistake from a hallucination. So it is unclear to me (and presumably others) what the precise distinction is to you and Simon.