No, I certainly think not, because what I think the bill is fairly clear in is that it really is emergency first responders, whether it's fire, police, ambulance, or, as you say, search and rescue.
Emergency first responders, regardless of the occupation they're in, are on call. It's not like where a child goes lost in a community and you put out a notice asking people to volunteer to help.
They are documented; they're on a list. The answers that the fire chiefs gave maintain that the record-keeping would have to be under a municipal authority. That might be delegated to a fire chief; it might be delegated to the head of the Coast Guard Auxiliary, or whatever.