SAR (in Colorado at least) does not, and hopefully never, will charge any rescue subject a dime. I've been on more than a few missions where the subject initially refused assistance in fear of being charged but immediately changed their minds when informed otherwise. This is a scenario we all want to avoid.
SAR organizations are all volunteer and are required in each county by the Sheriff's office.
But if you accept a heli evac from an air medic service, your health insurance almost certainly will be billed (a lot).
I'm not positive about billing for a HAATS evac but I believe you won't be charged for that.