Public land is governed, and is regulated, and access to public land can and has been limited by the government on many occasions over the years. We are often "permitted" to enter public lands to do various actions. Even if you own land, you are subject to regulation of what you can and can't do with it (try draining a recognized wetland on your property and see what happens).
Hiking, biking, camping, hunting, fishing, logging, gardening, conservation, mining, dumping garbage, you name it. Whatever action you want to take on public land, such action can be restricted at anytime by the government, including just stepping foot on it. That makes it a privilege. Abuse it, and you will lose it. Private land ain't much different. A little thing called "Eminent Domain" allows the government to come in and take your land anytime they feel like it. Yeah, you might get paid, but it will be whatever they think it is worth, not what you say it is. And the government can come onto your land anytime they want to, and not only can you not stop them, but if you should try, they can use lethal force against you (as much as it takes to get the job done) and nothing will happen to them.
We have darned few rights these days, a lot fewer than we had a hundred years ago. Last I looked, going wherever you wanted to and owning real property wasn't listed in there. You have the right to pursue it, but not necessarily to ever obtain it.
Was the kid wrong? You bet he was. Did he screw up? Without question. Was the extraction warranted? Based on all available information, I doubt he'd have survived let alone self-rescued without it. Is the fine excessive? The expense is probably justified, but I doubt they'll ever get that out of him or his family. Whether they ever imposed such a stiff fine, or any fine for that matter, on anyone previously rescued in such a manner is irrelevent in court. The law as published provides for application at the discretion of the agency involved, and likewise enforcement is non-obligatory, so that argument is moot. I am quite certain that if they were compelled in court to come up with a list detailed the costs, the fine would likely increase considerably. I doubt any sane lawyer would lead their client down that garden path. The agency will have no problem subtantiating the costs. As for use of non-agency services, that is done all the time, and that is how the agency meets it's obligations in a budget tightened economic cycle. Lots of agencies keep private contractors on reserve for emergencies. Another moot issue.
I expect this to lead to would be adventurers making more solid plans about their expeditions. Maybe, to avoid the high cost of government involvement, I expect someone will provide private SAR services for a subscription fee and if their client gets lost or hurt then they will be the ones contacted and they will be the ones doing the rescue (with commensurate liability insurance coverage should things not work out for the best). Either that, or maybe adventurers will do more to ensure they can self rescue or have friends/family available and properly equipped. The other and more likely recourse, given the laxidaisical nature of the general public towards self-accountability, is that some form of adventurer insurance will become mandatory just like getting a vehicle licensed requires proof of insurance.
Pick one. It is inevitable, Mr. Anderson.
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The ultimate result of shielding men from the effects of folly is to fill the world with fools.
-- Herbert Spencer, English Philosopher (1820-1903)