If grown-ups have a personal umbrella insurance policy, on top of their underlying homeowners and auto policies, wouldn’t the umbrella underwriter pay for reasonable charges assessed against the named insured by the rescue service(s) if its uncertain whether negligence is involved (or even in the case of gross negligence), or wouldn't the underwriter at least pay for the legal defense of the insured? Sure wish one of the fine attorneys on this site would brief this issue (in light of the language in several randomly selected umbrella policies).
If you have umbrella coverage, New Hampshire would certainly go after your insurance provider and most NH courts would informally limit recoveries to the extent of insurance. In effect, everyone who is a named insured in an umbrella policy is a first class citizen in that they have pre-paid their "rescued while negligent" assessments (but would still be subject to loss of NH driving privileges, darn). My take is that any time the person rescued has been drinking or taking drugs (such as dope for ADD), he or she is or would be deemed, for better or worse, automatically negligent, so he or she pays for the search & rescue with PayPal.
State Farm and All State in my state, surprising cover a number of risks that are not otherwise covered by underlying policies, such as non-business related libel and slander (who would have guessed?). (However, I still advise grownups to never talk to a newspaper reporters, but I'm just a kid and what do I know.) No other type of non-business insurance that I'm aware of covers liable and slander.
Could Lloyds be persuaded to write search and rescue insurance, to be sure? Good question. There are some Hunting Club Liability Policies that I've seen that are sure knocking on the door of covering these risks if the search is related to hunting club pursuits, whether on public or private land.
Why doesn't the Eagle Scout make a reconventional demand against the park (F&W) service and/or the rescue agencies? In my part of the country, the Eagle Scout would not only have an excellent case, but he'd also be handsomely compensated for his pain and suffering [including, but not limited to the mental anguish suffered by the implementation of an arbitrary $25,000 fine (i.e. rounded up to the nearest $25,000 --- seems as if in NH public officials like to round a lot, but this is the price the NH citizens pay for under funding the school system for so many years)]. If I were an Eagle Scout, I'd settle for $2,500,000, an apology from the Governor on behalf of all NH citizens, attorney's fees and the immediate resignation of the Executive Director. The park service would then think a lot more than twice before drawing more incoming by recklessly implementing more of these nice, fat & round fines in $25,000 increments.
Where this is heading is that people are going to think a whole lot before they even consider calling for help if he or she, a family member, friend or someone they don’t know is or could be lost and injured or lying very very still, especially while in the dark, damp, cold, tick infested New Hampshire woods. This is going to greatly lessen the need for volunteers and paid rescue services. It will also lessen the reason for being of the national and state park systems, or at least their bloated staffs, and I’ll have you know its for the greater good. Not only the victim but the caller or person who “stupidly” reports the potential wildernism emergency could be held liable for fines and the cost of searches, and the caller could be subjected to hard time. On my solo mis-adventures, and in light of my helplessly meager resources (no thanks to the repressive child labor laws), the only time I'd be calling for rescue would be when there is a lot less than remote chance, god forbid, I can claw my way out.