Speaking as an old SAR guy, I don't think any rescuer would consider time spent assisting you as time spent frivolously. Many times we went out, typically looking for overdue people, finding them working their way back home, behind schedule for any of various reasons, but definitely still functioning. They would have gotten home on their own, and all we did was resolve the anxiety and provide a little encouragement, a drink of water, and a bite to eat. None of us ever considered our time wasted.

Instances of "SAR triage" were rare in my experience. When they occur, you deal with them as best you can....