Accident – Rent a car – Without police

Hello everyone, there’s a little problem. I was driving backwards in a parking garage in my car the other day. The problem with the whole thing is that the causer was on the way with a rental car. However, he had no damage. On his push we arranged the whole without police and he signed me that he was responsible for the accident. After I was in the workshop now and the damage is probably more expensive than expected he wants the ga The car rental company says, however, that you do not pay for the damage, since the police did not take the accident. What to do now? Does the insurance have to pay even if the police were not on site? Do I still sit on the damage now although I have a confession of guilt? Does the accident causer have to carry the damage from his own pocket? Maybe you have some good tips for me. Thanks already.