The stochastic parrot framing makes some assumptions, one of them being that LLMs generate from minimal input prompts, like "tell me about Transformers" or "draw a cute dog". But when input provides substantial entropy or novelty, the output will not look like any training data. And longer sessions with multiple rounds of messages also deviate OOD. The model is doing work outside its training distribution.
It's like saying pianos are not creative because they don't make music. Well, yes, you have to play the keys to hear the music, and transformers are no exception. You need to put in your unique magic input to get something new and useful.