Well, first let me say I'm sorry you had the accident and that I'm really, really glad that most of the damage was removed.
I guess how the kid acted at the time of the accident and how he is owning up to the accident is how I would pursue it.
If the kid was very apologetic and still fesses up to the accident, no BS about I didn't hit you or anything, then I would let it slide. Let it be a learning experience to him and make sure that you give him a lecture about this (You're entitled, he hit you!). YOu could have an estimate written up and kept on file but not go through with the actual repair. This way the insurance has this on his record but it won't effect his insurance and his rates won't go up. Also, the insurance may have a window period in which you can get the repair done so if you choose not to repair it now (assuming you get the estimate), then if you change your mind later, you can have it repaired if it looks bad to you still. (Check these things with the insurance company though!)
If the kid was a total jerk (which it doesn't seem to be) or if he changes his story, rake him over the coals and teach him he has to own up and be responsible for his actions.
Here's my story. I got hit by a lady earlier this year. I got her info, she was very apologetic. I got the estimate, didn't think it to be that much but it turned out to be $750. I was going to get the repair but was a little hesitant to begin with because painted bumpers usually chip upon the first impact and I hate to lose the use of a daily driver for a week. The lady called me and was so afraid that the insurance was going to go up because she didn't have much money. She was in her ealry 20's, had a new baby, spoke very little English, and worked part time at Dunkin Donuts. I felt very bad for her situation. The thing I thought about was about how God has mercy on us so we should have mercy on others. So I gave her a little lecture about this and told her to take care of the baby, etc... I called the insurance company and cancelled the claim and they stated that I have a 3 year window period should I change my mind and want to get the reapir...