> producing the statistically most "correct" output

That isn't quite how they work - there's a degree of randomness depending on so called "temperature". And it isn't the output that's statistically modelled, it's the next token based on the prior output.

> This sounds a bit like you are saying LLMs are conscious

No more so than OP is implicitly asserting that human art is produced in cleanroom isolation. I don't believe either to be true.