That sounds wrong to me. If your car is insured (as it is) I dont even know why the other insurance company is in contact with you at all.
Back when I had my EA, a lady backed into my car (while my car was parked) I was lucky enough to catch her before she drove off (thanks to my very noisy alarm). I bought the new bumper, indicatotor, and got my neighbour to fix the guard and spray the bumper and scratch on guard (he owns a panel beater place). I sent my receipts to Suncorp (my insurer at the time) and a little while later, I got a cheque in the mail for my costs.
I think they should be more happy to do it this way... cos that accident ended up costing 1/4 of the price it would have if I had just taken it to a panel shop to get the whole thing done.
FPV - Tickford Club of NSW