What the police officer did not tell you, is that IF you go through Your insurance company when the other drive is clearly at fault, Your insurance company must then activate their resources to go after the other drivers insurance.
Even if you were clearly not at fault, Your insurance company treats the claim processing as a claim incident or " involvement" on your records.
Now lets say that the next time it IS your fault, as far as they are concerend you've already been "involved" in 2 accidents.
Now if the other driver does not have insurance or if his insurance lapsed for some reason, like non payment, then you would need to go after him through your insurance company.