此人
1.was driving very slow
2.sudden cut in and stopped in front of you for no reason
3.you reacted very fast to stop the car
Don't admit it's your fault. Let the insurance company find out. This guy may be subject of insurance fraud but the conclusion will be based on the fact, witness, and his record, I guess.
You can try to consult a lawyer for free. But since the damage was very limited and no personal injury, lawyer will not think there is a case.