Should you file an accident claim with your insurance company if you were not at fault?

Yes, if only to have your side of the story on record. Do it.

At the very least, phone up your insurance company and tell them exactly what happened and get their advice. They will be happy to talk to you on the phone - this might not involve making a claim, but at least they will have a record of your version of events.

If you do not do this, then later who knows what kind of skeletons could creep out of the closet - guy turns up wearing a neck brace etc, and it might be too late for the insurance company to protect you then.

A

Always, the other party might lie and you might get an At Fault accident record. Always call