Humans can't claim ownership, but they are still liable for the product of their bot. That's why MS was so quick to indemnify their users, they know full well that it is going to be super hard to prove that there is a key link to some original work.

The main analogy is this one: you take a massive pile of copyrighted works, cut them up into small sections and toss the whole thing in a centrifuge, then, when prompted to produce a work you use a statistical method to pull pieces of those copyrighted works out of the centrifuge. Sometimes you may find that you are pulling pieces out of the laundromat in the order in which they went in, which after a certain number of tokens becomes a copyright violation.

This suggests there are some obvious ways in which AI companies can protect themselves from claims of infringement but as far as I'm aware not a single one has protections in place to ensure that they do not materially reproduce any fraction of the input texts other than that they recognize prompts asking it to do so.

So it won't produce the lyrics of 'Let it be'. But they'll be happy to write you mountains of prose that strongly resembles some of the inputs.

The fact that they are not doing that tells you all you really need to know: they know that everything that their bots spit out is technically derived from copyrighted works. They also have armies of lawyers and technical arguments to claim the opposite.