Yes, quite a coincidence…
Regardless of what they say on the phone, make sure you get it in writing - you don’t want to wind up in a hassle with them after you’ve had the repairs done because you didn’t get 7 estimates including one from Mongolia, or your mechanic didn’t use the brand of paint they recommend, etc.
My experience:
I was rear-ended last spring. The guy immediately admitted fault, both to me and the cop who came to check it out.
I called my insurer just in case, and they told me I could go one of two ways: file a claim with them and let them figure it out, or see if the other guy’s insurer would pay. If I went with the former, I was told my rates might go up. I decided to wait.
By the end of the day, the other guy’s insurer (GEICO) had contacted me, told me that he had admitted fault, and that they had agreed to pay all damages, give me a free rental, set me up with an adjuster, etc. So there was no need for me to go through my insurance at all.
If there had been a dispute, of course, I would have let my insurance deal with it.
A couple of months later, my wife was rear-ended. The outcome was the same (other driver admitted fault, her insurance paid everything), but my wife did file a claim with our insurance. As far as I know, our rates didn’t go up. So I guess it could go either way.
My dad got rear ended, Then his car was hit by a drunk driver. The insurance company raised rates claiming he was “accident prone.”. In America we have to fear our insurance companies.