After self-inflicted accident: Reviewer of the opposite side wants to settle with me directly

Hello, at the beginning of December I had an accident caused by me. I reported my liability insurance. Until the recalculation of the SFR I did not hear anything from my insurance company or from the opponent of the accident. Now I received a letter from an expert who presented himself as an expert ordered by the opponent of the accident and informed that only € 680 of the costs of the expert were transferred by my insurance company. was “valued” as an “unfounded excuse” and therefore you now demand the balance of 120 € + 50 € additionally incurred processing costs now directly from me and I should apply for reimbursement directly to my insurance. What wurmt me about the thing: 1. An invoice / composition of the costs is not before me 2. The “unfounded excuse” was not carried out further I do not want the accident opponent to remain at any cost but I ask myself , whether it is wise to pay the claim itself here. Of course I will try to ask the “unfounded excuse” of my insurance and get further advice there but is this procedure in some way justified? Why do I have a liability insurance insurance if in the case of damage not all costs are reimbursed to the accident opponent? Bzw. doesn’t the expert have to argue with the insurance?