Many years ago I worked on a volunteer ambulance. Us volunteers didn't get paid, we did it for free. However, we bought a small building to house two ambulances in, that also had a central living area for our crews. We slept on the floors in our sleeping bags. We bought two ambulances. They cost $80,000 each (this was back in the 80's). That as just the base cost of the vehicle. We then had to buy radio systems, O2 setups, defibrillators, etc. and arrange for the local police to act as our dispatchers. All medical supplies that went inside the ambulances were extra cost. Many of those supplies had short shelf lives and had to be replaced often. The local hospital graciously supplied us with the required "physician adviser" at no cost. The ambulances required gasoline to run, and also routine maintenance. For long term volunteers (years of service) we provided training free of cost as a thank you. I had my Paramedic school paid for like that. Of course, we had to serve additional years after that training was paid for. We got zero tax dollars.
How could we do all that "for free"? We couldn't. Volunteers bought their own personal uniforms and supplies, but asking them to chip in to buy buildings and vehicles was a tad too much. So we had "memberships" that we sold every year. For $20, I think it was, you, your family, and any guests in your house received unlimited ambulance transportation for a year. The local newspaper was great and published nice articles every year during our membership drive to generate interest in the town. Townsfolk who didn't want to participate were billed if they called us for transport, and got to figure out how to pay in conjunction with their insurance companies. Our bills were cheap compared to other for-profit ambulance services in nearby areas, but a single bill could easily run into the 100's of dollars. If our patients didn't pay, we didn't advertise the fact, but we just wrote it off as a loss and prayed that we'd have enough money to continue operating.
For SAR, I would propose something like we used to do. At the state level, offer a "rescue membership" for a fee. The state then would dole out the money to the various SAR operations. For the victims who chose not to participate, bill them. And then on an individual basis, decide what percentage of the bill would justifiably be written off based on the actions of the victim, their self-entitlement appearance, their attitude, how stupid they were to get themselves into the predicament, etc. Jerks don't get freebies, but normal people who made a genuine and understandable mistake might.