How is this any different than, let's say, a county government billing the family of a murder victim for their investigation? It makes no sense.

Search and rescue teams are government agencies (at least here they are). There are private companies that do this - and if the family so chooses to hire them that's on them - but the government agencies that search and/or investigate are paid for by our tax dollars (please, someone correct me if I am wrong).

Even if the family is mega rich (which I believe the Fossett's are) it makes no difference. If it were your family member out there would you want someone checking to see how much money you had before sending help?