What regularman said. Why in the world are you dealing directly with the hit-ee rather than with their insurance company? Was he insured? Do you have uninsured motorist?
Also consider that YOUR insurance company probably won't be happy if you do an "on the side" repair either. Some day maybe you get hit again, it goes through the right channels, and the other insurance company says, "Well there's already previous damage here so we're not going to pay for a full repair."
Also consider what happens if you do it yourself, and misdiagnose the full extent of the problem. Maybe later you realize the frame is bent. Are you going to go back to the guy and ask for more money? Just live with it?