There seems to be two issues here. Should the ship that is rescuing her charge her parents? No, because that is the law of the sea, you respond to a distress signal, BUT this distress signal was passed on along by a SAR effort that IMO the parents should pay for.
Here's a question I have , and I really don't know. Could the ship that rescues the brat claim her ship as salvage?
Last I heard, as long as it's in international waters, yes.
The parents shouldn't pay for anything. Maritime law is not about money. Sea Air Rescue is exactly as advertised. The law came about before SAR existed.
Are you aware if you are CPR qualified and leave the scene of an auto accident you can be charged? We have a few rules and laws that apply to all. At least anyone civilized.
You don't leave someone to drown or bleed to death because of your payload.
We lost about 5 days on one deployment looking for a bird that went down, just because. It's not about pointing fingers. It's about saving lives.