If you are worried about the company claiming rights over your personal work, then it is prudent.
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.
Then I realized how stupid that was even though my employer was fine with and was never strict with how a work laptop is used.
I realized not only did I not want my work to know what I'm doing on my personal time, the risk of cross-contamination and being accused of stealing confidential documents or a personal text making it look like I'm doing something wrong is too high.
I bought my own cell phone and laptop and now never use my work equipment for anything but work. Not worth the risk.
If they wrongfully accuse you of that, isn't it a place you should leave in any case?