They only take from the statistical distributions of words in the context of preceding words (which is why they never say "the the" etc, why the grammar is nearly always correct). But that doesn't mean that whole sentences are lifted from the source material. There are near infinite paths through those word distributions, and many have never been produced by humans, so LLMs do produce sentences that have never been uttered before.
They couldn't produce new conceptual context spaces in the way that humans can sometimes, but they can produce new combinations within existing context spaces.