The VP didn't just say "no", but also ratted me out to like the six managers between me and him, and each manager thought it was a good use of company time to schedule half-hour meetings explaining to me that I needed to go through the proper bureaucratic channels because the VP's time is "extremely valuable". Honestly kind of poisoned the entire job for me.
It was ridiculous.
Every time I've done this, they've agreed to the change. If they don't, then I don't take the job.
Hope you did it anyway. No one should be able to tell you what you can do in your spare time.
I mean, I wasn't worried about them suing me for contributing to open source (it would be pretty hard to prove any real damages), but I think being fired would have been on the table.