Bullsh--. If she doesn't like it she should move out. I can't stand anyone who has no problem mooching off mommy and daddy yet thinks it's unfair to live by their rules. Take the good with the bad. You don't like it their rules? Great no problem, then move and make it on your own. Welcome to the real world.
No she shouldn't "need" a chaperone. But if that's her parent's wishes, she should respect them (which it sounds like she's willing to do, and I give her that much credit).