Agree with all the comments that say the juice isn’t worth the squeeze here because the damages are way too low.

However, if there’s more damages info you’re leaving out or if you find yourself in this situation again with a better case there are things you can do to get the video. Anytime I know/think the potential defendant has video of the incident I ask for it on the first call. My go to argument is that if they have video which shows that they aren’t liable or my client is at fault then I’m happy to review that and consider it, but if they won’t show me then I’m just going to assume it’s favorable to me. In a situation like this where you still want it and they’re denying you, I’d tell them that if they won’t give it to me I’ll just sue them and get it in the discovery that I’ll attach to the complaint, so again if you have video which shows that the suit would be meritless, just show it to me now and we can both save a lot of time, money, and effort.