...This is unusual and not really the best move if they are simply rendering medical aid on a crash (would make more sense if something were on fire)...
Do you work for an ambulance service or a fire department? You do understand the difference between a human life and burning car right? One can be replaced, the other can't.
Maybe I am not understanding your definition or use in your post of "rendering medical aid" but every vehicle accident I have been on we evaluate the mechanism of injury, and often rely on initial radio reports to try and help evaluate what we might encounter on scene. I've heard some stupid shit coming from dispatch from untrained people on scene giving initial reports. You can't really rely on it. Now, if I know I can trust the reports and that they are from an officer I have worked with and trust? I'll listen and take my hairy hair shirt off
Sometimes the most mundane of accidents to the untrained person might seem like "no big deal," but I have seen people who were walking and talking turn south pretty quickly from unseen internal injuries. So there is ABSOLUTELY the need for trained medical personnel to arrive on scene and evaluate the patients as quickly as possible.
Imagine for a second that the fire truck went to the next exit and came back around to the scene. Imagine that that took another 5-10 minutes and in that time the patient died. Who would be fucked then?
I've been in the right seat of a fire truck. There are a MANY things going through my mind when arriving on the scene. Scene safety, parking, not running people over that might have been ejected, fire and other hazards, and patient access. Hopefully, my decision on where to park offers the maximum protection from oncoming traffic to my crew, but at the same time doesn't cause additional accidents. If that happens, I made a bad decision. But...at the same time, I don't want to have to explain the decisions about my parking to a CHP on a hot scene. We can have that discussion later (and I have had my lectures).
If I arrive at a vehicle fire and it's vacant and fully involved? Fuck it, I'm not saving much, so crew and civilian safety is #1. Putting out the fire would just be training, not saving anyone any money unless there are secondary structures involved.
Most of the arguments I've had with the popo on calls is when they are trying to turf drunks off on me for medical evaluation. I hate that, especially when they are combative (like from domestics) and wind up making me put them in a backboard taco and use up all my duct tape
