2) That’s definitely a valid point. I have worked on free/open-source code for most of my adult life. For a long time, it was for my own use, but I started publishing code for use by others, and provenance became a much more important coefficient.
Honestly, of the two scenarios, this one is the more likely to fall on the employee's side.
We haven't really tested the legal precedent for ownership of LLM outputs very thoroughly yet, and I'm willing to bet a bunch of us still have employment contracts that haven't been updated to cover LLM use...
It might be overly paranoid depending on what the circumstances are, it might be a real concern as well.