> That you can't copyright the AI's output (in the US, at least),

It's also not really clear if you can or cannot copyright AI output. The case that everyone cites didn't even reach the point where courts had to rule on that. The human in that case decided to file the copyright for an AI, and the courts ruled that according to the existing laws copyright must be filed by a person/human/whatever.

So we don't yet have caselaw where someone used AIgen and claimed the output as written by them.

You can copyright AI output assuming there is a "reasonable" degree of human involvement. https://www.cnet.com/tech/services-and-software/this-company...

Yes. And that’s why the rules say that the human submitting the code is responsible for preventing this case.