Liability damage: free choice of assessor vs. obligation to minimize damage

Hello, I was assumed to have been caused by a car accident, the damage to be seen in the picture (+ paint scraps side mirrors + contact traces on the tire). Am I “obliged” by my damage minimisation obligation to keep the damage for the opposing insurance low and only to have a cost estimate made instead of an expert report? The car is EZ at the end of 1996, BMW 316i Compact with approx. 200tkm. … who can tell me something about this? Thank you for your help! PS: It is also difficult that the cause of the accident was not very friendly and above all not reasonable. That is why the police were consulted. In my opinion, the police have clearly said who is considered to be “guilty” and also told the supposed causer what he could get set up (80 EUR + 2 points).