It may be too late now, but, I wouldn't have closed the incident with your insurance company. I'm sure the $500 deductible that you'd be paying up front was part of your consideration.
About 10 years ago, someone backed into Mrs. Alpinemaps' car. We got the insurance info, called it in, and then did what you did - cancelled it when her insurance company said 'no problem, we'll take care of it.'.
Well, don't forget who her insurance company works for - her. They don't work for you. The body shop wouldn't release the car to us for days, because her insurance company wouldn't pay them. (This was the body shop that her insurance company suggested we use, which was fine with us, because we had used that body shop before).
When I called my insurance company and asked them to help, they just laughed - since I didn't have an open claim with them, there was nothing they could do for me. They weren't working for me on this.
The smallest amount of inconvenience, IMO, is to let your insurance company deal with everything. They'll get you your check in the end. Yes, you'll be out your deductible for a small amount of time, but you will eventually get paid back. You'll have someone working for you on your side of things (including their lawyers) if it ever comes to that. (Doesn't sound like it's a big deal in this case, but for anyone else listening...)