try other shops also there can be more damage the you see
Unfortunately you do not have the upper hand, although you can argue that the bumper and/or absorber should not be affected; only the paint/clear coat. For the other driver/owner's peace of mind, they included both.
I did the same about 8 years ago, and I paid $700, which also included a rental car.
Some people just don't have reasoning/heart. Good luck!
Shop around There must be more than one repair shop
go to the shop and look at the estimate
A few days ago, I rear-ended a car in stop and go traffic at about 4mph. It left a clear, but small scratch, and did not result in any dent. The other driver and I took pictures and exchanged insurance info. She took it to a shop for an estimate, and the shop wants to replace the absorber and rear fender as opposed to re-painting it. This clearly isn't necessary, but I don't know how to proceed from here. I haven't made a claim yet, and would like to avoid doing so. Aside from demanding photos of the parts needed to be replaced, what else should I do?