I think it’s bullshit too.
FWIW, my (large) company has a policy where you submit requests to conduct outside business activities through Compliance, so in this situation you’d go to this link and tell Compliance what you want to do and that there’s no conflict of interest, and I think they’d approve it. You might mention it to your boss as a courtesy, or not. If it’s something you’re doing outside of working hours and doesn’t interfere with your primary job, who cares.
I do think you could have another conversation with your boss and say you’d really like to pursue this opportunity, and who would he recommend you speak to in order to get it approved, given that the policy is changing. You might want to speak to an employment lawyer before you do. In my experience it’s ALWAYS been worth it to spend a couple hundred bucks to get their advice before going and having a conversation, so I know my rights and what to ask for.
Your boss probably feels like he owns you and doesn’t want anyone competing for your time. My boss is like that. When I first started here, I signed up to work for her as a contractor 30 hours a week and I was already working for another company (someone she knows and respects) part-time as well. She ended up wanting me to work full time and I was giving the other guy a lot of time too and I ended up gaining a lot of weight and being a bit of a wreck (this was during lockdown which made it even worse). When she had a FT position to offer me, to convert me from a contractor, she made me promise I would no longer do ANY work for the other guy. So petty. I don’t think your boss would be swayed by the arguments CG suggested. It’s something you could try if you were very confident about leaving that place but otherwise I probably wouldn’t.