My take on this is that you can deny liability on solid legal grounds and tell the person that they were contributorily negligent and thus have to cover their own damages.
If they actually want to try and press the case, you then turn it over to your insurance company and ask them to defend the case based on your denial of fault.
However, this is not the sort of thing that a lawyer would work on, and they would likely have to bring the claim in small claims
court. If they did so, you could simply at that point either agree to pay, turn it over to your insurance company, or go to court and deny liability and assert that they are contributorily negligent (I think you would win).
In regard to your insurance. A small damage claim like this may still cause your rates to go up. But this is entirely up to the insurance company and depends on your claims history. If you haven't made any other claims and have a good driving record, a small fender bender like this may not affect your rates.
You can contact your insurance agent and ask them about what they think about whether this would cause your rates to go up or not.
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