There is a fine line between hallucination and creativity. When we know the exact answer and seek it, we label misfires "hallucination". Is it that the answer

There is a fine line between hallucination and creativity. When we know the exact answer and seek it, we label misfires "hallucination". Is it that the answer was not in the data set? Or that the LLM chose not to use it? Or something else? I find it ironic that people claim LLMs are creative and then tryy to eliminate hallucinations. Maybe we need an explicit switch to turn on/off creative elements in general