Haha, yeah, I thought it was funny. I found this out when someone threw a backie off a jump that was wearing similar outerwear to me and ski patrol caught up to me and asked if I did it and I said no, then I felt the need to ask "what is considered to be an invert" and he replied "nothing with your feet above your head", but then the ski patroller right next to him said "well, basically no Backflips or Frontflips, everything else is cool".
I still do fronts off rollers and stuff, but I make sure no patrol is around first - it's harder with backs because the lift goes right by all the jumps that are backflipable and you can't really tell who's on the lift cause it's not just patrol that needs to catch you, basically any employee can call up patrol and tell them to get you and you can't always tell whose working and who isn't.
While it's true that you aren't putting anyone else in danger, it still has to do with "public safety" (seat belt laws are the same thing basically - you're not hurting anyone but yourself, but you still are part of the public). Plus, it's all about liability, you can get really hurt doing inverts and lawsuits can be huge money, if they don't allow them then they have less of a chance of someone get permanently injured. Plus, it keeps insurance costs down if you disallow inverts.