Search and Rescue does not charge. They are an emergency service like the police, not a private ambulance company. Someone correct me with the appropriate references if I am wrong but as of now there are no reimbursement costs associated with SAR in the US.

Keep in mind this is different than life-star or other medical billing which would fall under your personal/health insurance.

I do stand partially corrected; a bit more homework and some states (individual laws) allow for the recovery of expenses if the party being rescued is reckless or negligent. IE: getting drunk and plowing your 4x4 off a jump or something. This would not apply to things like breaking a leg on a trail, snake bite, that sort of thing.