Oh, no man. The potential lawsuit is a completely different issue. hahaahah.
This is simply for medical reasons because homeowners insurance covers up to a certain amount for people injured on your property.
In my hypothetical situation, OP's parents would not only pay the increased premium because of all the medical bills their insurance paid for, but they would ALSO probably be sued by the friends' parents for another large sum of money. For what, you ask?
-You weren't supervising and inverted aerials aren't permitted - Negligence
-Your tramp has no pads around it and no netting - Improper safety precautions
-Your child was pressuring mine to do a trick they weren't comfortable with - bullying
The list continues.
Moral of the story? Kids, when your parents tell you they will NOT buy you a trampoline.....just say ok and be happy they still pay for your Saga.