That's not how it works. If you ask an LLM to write Harry Potter and it writes something that is 99% the same as Harry Potter, it isn't magically free of copyright. That would obviously be insane.
The legal system is still figuring out exactly what the rules are here but it seems likely that it's going to be on the LLM user to know if the output is protected by copyright. I imagine AI vendors will develop secondary search thingies to warn you (if they haven't already), and there will probably be some "reasonable belief" defence in the eventual laws.
Either way it definitely isn't as simple as "LLM wrote it so we can ignore copyright".
(From what I understand, the amount of human input that's required to make the result copyrightable can be pretty small, perhaps even as little as selecting from multiple options. But this is likely to be quite a gray area.)