>This requires hallucination, because it has to make up things. The story has to be original.

Is it a hallucination if the story is original? There's a difference between "what's the rest of this famous poem?" and "let's just make poetry".

It is irrelevant for the point being made: LLM does exactly the same thing in both cases - generates statistically plausible text, based on examples it was exposed during training.