Auto Insurance Claims: how to handle minor bump up, metal bumpers, nissan x terra

Question
My teenage daughter backed into a 1995 ford Explorer with here Nissan X-terra. The police were not called and no accident report has been filed. The damage to her X-terra was very minor, only a slight dent in the plastic piece on the right rear corner. I was able to easily pop this back out. The other car was hit on the right rear corner. She hit the bumper and taillight. The tail light will need replacing, the bumper will need adjusting and there is a nicle size dent just below the taillight, but no paint damage. The owner of the other car got an estimate of around $700 to repair this. Based on my 35 years of restoring and repairing cars, I think this estimate is high, but I'm not in a position to argue this estimate.  

Here is my question. Should I pay for his damage without going through my insurance or should I let the owner of the other car file an claim with my insurance?  

Answer
$700 to repair what you've described sounds like a deal to jump all over.  I'm lucky to get a body shop to touch anything other than a scratched plastic bumper cover for less than $1,000.

Metal bumpers are rarely adjustable. They bend.  If they are chrome then they cannot be bent back.  If they are painted, they will likely need refinishing after repair due to the tool marks.
The lower section of a 1/4 panel is usually too thick to repair using "Paintless Dent Repair" methods (such as with door dings) so most repairs will be traditional methods which, as a car restorer, you already know involves the destruction of the finish.  The application of the two stage finish will involve clear coating the entire panel, which cannot be done without removing the 1/4 glass due to problems with clear coat adhesion on the edges.  

I get a couple of these a month where the at fault person presents starts out as a nice guy and presents a reasonable repair estimate.  My insured then refuses to pay it and ends up with a claim against their insurance and a subsequent rate increase.  All you have to do is write a check and this goes away.  Or, you can complain about the amount and they will file a claim against your policy.

Now where'd you put that check book? :)
Good luck!