You are wrong. AI has done mathematical proofs that were new. It *can* only be original by combining existing information into new patterns, but if the "rules of inference" are good, this can allow it to create something new and good.
OTOH, you are partially correct, in that it can't derive anything that wasn't already implicitly implied by the existing knowledge.,,because it can't currently run its own experiments.
N.B.: This is a comment about "AI" not about pure "LLM"s. Pure LLMs are a lot less reliable, because they've been designed to never admit that they are uncertain. And because they've been trained on the Internet.