Kinda happened to me once, got rear ended on Park Ave in Linden, the driver came out and was apologetic but then became upset once he saw that I was calling 911. I did the opposite of what you did, first got his license plate, then did not move my car.

One cop was annoyed that I was blocking traffic, the other filled out the report and was able to ID the other vehicle based on the Info I provided.

Good luck to you.