We do a surprising amount of "hallucinations" without the extreme version of hallucinations. We assemble things we sort of remember into incorrect statements all the time. I'm sure every one of us has been corrected for misremembering something or stating something based on misremembered facts (plague of clickbait headlines).

This is more or less how I see the LLM output, but as a path finding exercise over next-token probability graphs. This is (i.e.) why they are trained to use phrases like "wait but" or "actually", these words even out the probability of different paths, giving them their ability to "consider" different solutions.