There was a situation in Florida a couple of years ago where a nutty lady decided to go on an around-the-world sailing trip. The local Coast Guard commander physically confronted her on the boat and told her he'd arrest her if she tried to leave port. I don't know if he had any law on his side but he sure had common sense...

(this isn't the 13 y/o Dutch girl - that girl apparently has enough solo extended-duration experience to make it if nothing went wrong - the Florida woman had no experience at all)

As for "Duty to Perform" this recently was heard by SCOTUS and police officers can't be sued for not performing (the case was over a protective order that was not enforced). I didn't read the ruling and have no idea if it covers SAR personnel who are not police officers.