Towing Issues: Damage done to vehicle by tow company, aaa member, tow company

Question
I live in Riverside, CA.  I required roadside service due to a flat tire.  I am a AAA member and this particular tow company was sent out by AAA.  During the process a center cap that comes out of the center of the rime was damaged.  I contacted AAA and they indicated that the matter needed to be resolved between the company and myself. The company was unable to find a center cap that matched the other three therefore installed a different one.  The one that was installed had a decorative item in the center of it.  I informed them that it was obvious that it was different and that they needed to find one that closely resembled the other three. I also informed them that if they were unable to fine one that matched my mechanic would replace all 4 with something similar to what I initially had for $60.  They did not want to pay that and they indicated that they would replace all four themselves.  The unfortunate part is that they replaced them with 4 matching ones that say Eagle Rimes across the center of the cap.  I informed them that they did not match the rimes and that my rimes were not eagle rimes and that they did not come close to what I had.  The company has refused to done anything else.  Do I have any other recourse?  Shouldn't they have to replace the damage with something similar if the same item cannot be found?

Answer
Well yes, AAA was correct in saying to deal with the tow company..

Yes the tow company is the one that is usually responsible for damages, but I also have to say one thing here..
Some special parts such as center caps are hard to find at times that match the exact ones that you had..

Now also in defense of the tow company it seems that they are trying to handle it, but it seems that they are not doing what you feel is right about it...  Are you looking for the "EXACT PARTS" that you had, maybe they can not find them.  Are the ones that your mechanic can find the exact same ones you had on the vehicle. Your statement says that they are not the same. Are those ones even available anymore.
Also one issue is that most center caps are only available in a set of 4 not individual ones.

Oh yeah, I think from your question the tow company has tried to handle this, but one thing that most people do not know is that the "GREAT AAA" only pays the tow company something like $ 15 to $20.00 to do the services.. I am not defending the tow company, but you have said they bought you a set of all 4 already, how exact or similar do you want for replacement..

Sounds like they tried..  Sorry to say but you always have recourses...