I remember looking up towards the direction the car that hit me went and thinking, "please, please stop so you can call 911 for me," and the driver did stop and come back to me. He must have been in a state of panic, since he asked me, "Oh my god are you alright, can I do anything for you?" and I replied, gasping, "C-a-l-l 9-1-1".
In the ensuing minutes, a person with EMT training and a biker who was an off duty fireman stopped to check me out, make sure my hands and toes moved, made sure I didn't have pain in my neck, etc.
When a friend of mine crashed his bike descending Page Mill last summer (and fractured 3 spinal fins), a random car stopped for him and took him to Stanford hospital. Complete strangers!
You're absolutely right; give them an opportunity and people will show their wonderful side.