Creativity isn't well-defined. If you generate things at random, they are all unique. If you then filter them to remove all the bad output, the result could be just as "creative" as anything someone could write. (In principle. In practice, it's not that easy.)
And that's how evolution works. Many organisms have very "creative" designs. Filtering at scale, over a long enough period of time, is very powerful.
Generative models are sort of like that in that they often use a random number generator as input, and they could generate thousands of possible outputs. So it's not clear why this couldn't be just as creative as anything else, in principle.
The filtering step is often not that good, though. Sometimes it's done manually, and we call that cherry-picking.
Creative is when you ask a neural net to create a poem, or something else from "scratch" (meant to be unique). Hallucination is when you didn't ask it to make its answer up but to recite or rephrase things it has directly observed
That's my layman's understanding anyway, let me know if you agree