This is a question of principle. The objective is to gain the ability to rightfully claim "I have written this". There are a number of imaginable reasons to want this. Copyright, ethics, upstream project policy, you name it.

To put it to the extreme: Let's say I take the commit as is, typing what I learned verbatim off the screen as is but removing the "Co-authored by" note of the commit message. Then the LLM provider sues me, claiming I have no right to remote the note. Who would win in a court of law? I am not looking for binding legal advise here of course, I am just interested in what people here think.

To start off, law and ethics are not the same. Law is definitely not the extreme of ethics, I'd almost say it's the other way around. Law is just a practical (and imperfect) implementation of an ethical system.

At least in the U.S. (and the european countries I know of) only a human can be considered an author for copyright. Thus the code belongs to the person who prompted the LLM. As far as I know the AI-providers make no claim on the copyright of AI-assissted code generation.

Regardless, that is not what stops you. If you find this code online, in some repository that hasn't been upstreamed yet it is extremely likely for the code to be under some license.

Many of these licenses have no requirement for attribution at all, thus you can just copy the code no matter who the rights holder is. Some require that the code must be re-distributed under the same license, but if it was a change intended to possible be upstreamed that is already a non-issue.

This is my laymans understanding of the legal case, which is almost entirely separate for any ethical analysis (or principles).