To me that seems as pointless as saying "everything a person sees is a hallucination, it's just some of those hallucinations are true". Sure, technically whenever we see anything it's actually our brain interpreting how light bounces off stuff and combining that with the mental models we have of the world to produce an image in our mind of what we're looking at... but if we start calling everything we see a hallucination, there's no longer any purpose in having that word.

So instead of being that pedantic, we decided that "hallucination" only applies to when what our brain thinks we see does not match reality, so now hallucination is actually a useful word to use. Equally with LLMs, when people talk about hallucinations part of the definition includes that the output be incorrect in some way. If you just go with your quote's way of thinking about it, then once again the word loses all purpose and we can just scrap it since it now means exactly the same thing as "all LLM output".

> everything a person sees is a hallucination, it's just some of those hallucinations are true

Except it's not. People can have hallucinations that are true (dreams), but most perception isn't generated by your brain, but comes from the outside.