Have you ever had someone dent your car and apologize saying it was their fault till a cop showed up?

Its years later and I still get mad evertime I think of the guy who backed up into my car in a parking lot. I was easing out slowly and he was illegally parked on the side. It was evening and he decided to do half a u-turn by going back and he had his lights off. I wasn’t one foot out when he hit me. He gets out and admits it and wanted to exchange numbers without involving the cops. I told him I had to call the cops because it was the law. Needless to say when the cop arrived he told him I backed into him so it was my word against his. I lived in a no fault state so our own insurance took care of our vehicles. Luckily my insurance company believed my version since apparently he had a long list of accidents and I had none. I wanted to ring his neck. Would any of you have handled this differently? The cop took his whole story first and I could tell he believed his side of it. He only asked me for my license and registration and that was it. When I tried to tell him, he told me it would just be my word against his, so it wasn’t necessary. My insurance guy told me he was suppose to take a statement from me as well. Is that true?