The out of court settlements that avoid precedent don't mean anything in a broader legal context. Legally speaking, right now in the USA, output of LLMs is not copyrighted and cannot be copyrighted (without substantial transformation by a human).
I don't think this means the same thing as whether or not LLM output can infringe on someone else's copyright though (that does pose an interesting question -- can something non-copyrightable in general infringe on something copyrighted?).
Of course. I cannot claim copyright on a poem that I have memorized as a child and written down as an adult. The original author can, though.