Ummmh, sorry if this sounds political, so I am somewhat hesitant to post. Political commentary is not my intent, and I don't think this post is. Rather, this is one where my attorney background and experience kicks in and starts to define issues to be resolved, and policy issues involved. It echos cases I litigated over the years. So let me list a couple things that pop out at me:

1. Assume that the victim was unprepared/negligent in his preps for his climb, yet, could he still have been saved given a more rapid rescue?

2. Were any delays in rescue a result of bureaucratic/government negligence/incompetence/failure to define mission responsibilities, etc., even if the absolute time until rescue was pretty darn good (e.g. it could have been shorter without the delays)?

3. If the victim could have been saved with a more rapid rescue, AND the delay was a result of failures in #2 above AND the delay resulted in his death, what if any, damages should accrue to the family?

Note: in a philosophical/policy vein, holding governmental entities financially responsible for foreseeable failures & general incompetence/wrongdoing provides an incentive for them to reform their practices. So suing in a case like this may be seen as a way of forcing the various government entities to clarify responsibilities/coordination, despite the failings of the victim.

IMO, people screw up all the time; we have police/fire/EMS to provide a safety net when they do. When those services (appear to) fail because of bureaucratic "not my job" or "who's in charge" reasons, lawsuits provide one of the (sometime only) remedies that individuals have to bring the facts to light, and hold the government(s) responsible for their failures, and hopefully get needed reforms to help save people in the future.

Running down and verifying facts is what the lawsuit will do (hopefully).
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"Better is the enemy of good enough."