Precedent in the US is very much on the side of the person, not the method.
Whether the Xerox photocopier, the Sony Betamax or (so far) generative AI, judges are ruling that the fault in using technology to infringe copyright doesn't lie in the technology, but the way the technology is used by a person.
Generative AI isn't (yet) a person, so it is neither capable of creating copyrightable works, nor in itself infringing copyright.
I wrote a research paper on it, if you're interested.