I think where you are going wrong here is assuming that our internal perception is not also a hallucination by your definition. It absolutely is. But our minds are embodied, thus we are able check these hallucinations against some outside stimulus. Your gripe that current LLMs are unable to do that is really a criticism of the current implementations of AI, which are trained on some data, frozen, then restricted from further learning by design. Imagine if your mind was removed from all stimulus and then tested. That is what current LLMs are, and I doubt we could expect a human mind to behave much better in such a scenario. Just look at what happens to people cut off from social stimulus; their mental capacities degrade rapidly and that is just one type of stimulus.
Another problem with your analysis is that you expect the AI to do something that humans cannot do: cite sources without an external reference. Go ahead right now and from memory cite some source for something you know. Do not Google search, just remember where you got that knowledge. Now who is the one that cannot cite sources? The way we cite sources generally requires access to the source at that moment. Current LLMs do not have that by design. Once again, this is a gripe with implementation of a very new technology.
The main problem I have with so many of these “AI isn’t really able to…” arguments is that no one is offering a rigorous definition of knowledge, understanding, introspection, etc in a way that can be measured and tested. Further, we just assume that humans are able to do all these things without any tests to see if we can. Don’t even get me started on the free will vs illusory free will debate that remains unsettled after centuries. But the crux of many of these arguments is the assumption that humans can do it and are somehow uniquely able to do it. We had these same debates about levels of intelligence in animals long ago, and we found that there really isn’t any intelligent capability that is uniquely human.