A great story of military first aid training and initiative. Look not only did the military give me first aid training, but I have expanded training as Emergency Medical Technician. Too often as an EMT we would come to an accident scene where the medics were called quickly which resulted in more serious injuries than necessary had someone just taken the initiative to do something.
Under most state laws, you cannot be sued for helping (contrary to what some people would have you believe). Keep everyone as still as possible consistent with their overall safety (that is, if the car is burning or sinking and you can help-do so). That is not to say you should take unnecessary risks when trying to help someone, but even the simply act of applying pressure to a bleeding wound can do wonders. I once had someone tell me at a scene that they didn't want to use a dirty blanket to stop the bleeding for fear of giving the victim an infection. The patient lost enough blood that we had to re-start her heart on the road the hospital. The patient survived thanks to three units of plasma and short trip to the local hospital, but simply putting that dirty blanket on her leg would have done wonders for her health and recovery.
Look, unless your blanket is dirty by way of some fast acting poison, any infection someone gets from a dirty blanket is a far lesser concern than actually stopping the bleeding. An infection can be treated with aggressive anti-biotics. A loss of blood can lead to a loss of life.
Here is a funny story for you. In EMT training, I could not eat before class. The pictures of injuries made me squeamish (almost to the point of dropping out). But once I was onsight at my first car accident, I was never squeamish, there is too much to do.
So, if you come upon an accident, by all means call 911 and get the professionals rolling. Next, make sure bystanders are safe and if necessary stop or reroute traffic to make sure the victims are not hurt more. Then at least start taking an "inventory" of who is there and what injuries you can ascertain. Serious injuries should be brought to the professional's attention as soon as they arrive. Any information you can give is a help.