I was only a volunteer fire fighter about 1/3 of the way through Fire I when I had to move, but in order to go on calls, we had to have a basic level of knowledge. The first thing that my chief drilled into all of us was that we had to think of ourselves first. We had to make sure that our own gear was on properly before helping someone else and we had to make sure that we didn't put ourselves in a situation where the rescuer needed to be rescued. I would think that anyone in law enforcement, fire fighting, and EMS should have to follow that, especially if the situation is outside the scope of your job. The officer, while he meant well, should have waited until the FD arrived with the proper training and gear to perform a rescue. As to the FD arriving in full gear, in most places it is standard operating procedure to be in full turn out gear when you get to the scene of a car accident. I do think that the fire fighters should have just grabbed the officer under the arms and dragged him as opposed to taking the time to bring in a back board. I doubt that it would have changed to outcome though.
As far as dispatch goes, I know that they don't always have the correct or complete information to pass on. I also know that sometimes the dispatcher just doesn't have a clue as to what info you really need. Example, I went on a call with the FD to a fall with injury. I swear dispatch made it sound like someone fell out of a tree. What did we find when we got there? A sky diver...