I don't think that's a safe presumption at all. Getty, e.g., claims to have found their watermark in the output of Stable Diffusion.

More broadly, it's not a settled question of what license you need. The article presents a perspective that LLMs "would turn a Food & Wine review into a simple text recommendation of a bottle of Malbec, without attribution." I doubt that anyone has a license to republish the entire archive of the New York Times without attribution.

At the other extreme, I can "train" myself on newspapers I find discarded on the subway with no license at all. I don't need to cite my sources when I state an opinion based on everything I've ever read, seen, or heard. Is that a fair analogy to apply to LLMs?