What I did find is that BASE jumping is apparently often illegal (but definitely not everywhere per se), that everyone who did it can claim a “number”, and that 2000 numbers total have been claimed since 1981.
I’m not saying you’re wrong, I know next to nothing about BASE jumping. I’m curious what companies offer it commercially as an activity, and if that’s really widespread.
I just remember watching a documentary once, saying how crazy and uncommon it is.
The only place I know of where it's specifically illegal is US national parks (only national parks — you're fine in Bureau of Land Management and Forest Service territories).
Of course, if you have to trespass to make the jump, that's itself illegal, but that has nothing to do with BASE jumping.