When I worked in insurance, there was always a rule of thumb that said that the person who strikes you from the rear was always at fault. Nobody should be driving so close to someone else that they can't do an emergency stop. My boss always used to recommend (and I still do) that you write it all down now while it's all fresh in your mind, make some sketches, then report it to your insurance company - then if the other guy tries pushing for a claim against you, just refer him straight to them. It what you pay them for - but make the notes now while you can remember exactly what happened, so there is no doubt in your mind in a few weeks' time. You did right to stop, the analogy is that it could have been a tiny child running out in front of you, not a woman who should have known better, but that is neither here nor there - you stopped, he didn't.