Accident damage from third parties, my own insurance to pay?

At night someone drove against the parked car, also called the police. On the accident notice, however, only the damaged mirror stands, although the whole side had many deep scratches and dents. The opponents insurance recommended us by itself a contract workshop, which took up the complete damage and submitted it as an estimate. After technical approval we had repaired, only then. Now opponents insurance they only take over the mirror and the rest The workshop now wants to have paid more than 3,300 euros from us. Workshop now thinks it is possible to report the damage afterwards to the own cash insurance, in order to get back the amount paid by me then???? I have only partial cash and why should my insurance pay something where I am not the cause?? Is that so? Does your own (partial) cash insurance pay? Thanks for notes in advance