REAPER developer Justin Frankel, recently used AI to do all tedious work of studying the Ffmpeg API, AI gave code suggestions but some were wrong and he tweaked it. So per your logic, that code is public domain and Justin don't own that aspect of REAPER. Funny!
I don't think that's a correct assertion; if I asked it to modify some existing code that I owned the copyright for, that would not make the resulting modified version entirely public domain; the changes made would be, but the underlying code would still be subject to copyright protection. Additionally, if I modified its changes, then my modifications would also be copyrighted.
Perhaps a better way to look at it would be this: if you asked a LLM to write some new code according to a spec, then the resulting code (assuming it didn't directly copy some existing code which was copyrighted, which is hard to know) would be public domain. If a human then modifies that public domain code, then those modifications are subject to copyright, but the code prior to human edits is still public domain. So if someone were to copy the per-human-edit code, they could freely use it as it is public domain. Of course this doesn't address the fact that the LLM almost certainly ripped off some copyrighted (which could be copylefted for that matter) code.