I feel sorry for the victims. If I'm injured and scared, the last thing I want to see is the first responders argueing about my treatment. If I was about to go in to shock then that would certainly make matters worse. Remember why you chose this profession. I'm sure it wasn't for the lucrative pay. The question you asked in your post was "what would you do". I supposed my answer is that I would have stayed on the scene to help as best I could have and refrained from any confrontation with anyone else that might make matters worse for the victims. I also would have reported it to the on-duty personel when they arrived if in fact this did not take valuable treatment time away from the victims. I suppose in a nutshell, I would have put the victims' best interest above all else.

Now, having said that... I realize that this is one of those "easier said than done" type of situations and I don't think you should be discouraged that I (or anyone else) dont agree completely with your decisions. Right or wrong, you're human and will make mistakes. Furthermore you are to be commended not only for stopping to help to begin with but also for chosing a profession in which you selflessly give yourself to helping others in need!
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Learn to improvise everything.