IMO, try to negotiate up abit, but take the money and run. I had the same exact thing happen to me about two years ago, while I was living in Boston. A lady reversed into me while I was behind her at a light. She got and cried to me how sorry she was (crying women always get to me). She even told the cop how sorry she was. When I tell the cop to include this in his report, he says "reports are only to include what I see, not what I'm told." When I called the insurance company, I found out she had told them I rear ended her. It cost me $500 deductible to pay for my damage.