It would be a lie to sign those papers for something you vibe coded.
It's not just courtesy; you are committing fraud if you put your copyright notice on something you didn't create and publishing that to the world.
I don't just want that disclosed; I cannot merge it if it is disclosed, period.
If I use iOS's spellchecker which "learns" from one's habit (i.e.: AI, the really polished kind), I don't lose copyright over the text which I've written.