We also had an accident where somebody turned into us, but no witness.
I mean, in my experience that's the point where you put in a call to the local PD and get it reported, so the accident doesn't go on your record. If their car is t-boning your car, its a pretty clear-cut case of them being at-fault.
But if it was minor and folks were in a hurry and nobody cared, I definitely get it. Nice to live in a country that friendly and chill.