Car insurance companies will find any way they can to weasel out of a claim or pay less on a claim. This is one of the reasons I do not care for car insurance companies. Sorry if I sound bitter but that is just how I see it. Another BITOGER some years ago posted that "the insurance company is like a "good friend" who gives you an umbrella and then takes it away from you when it starts raining". That is a good way to put it.
The other thing to consider too is if OP puts this claim through his insurance, whether it is collision or UM or whatever, the insurance will report it to Car Fax or whatever agency they choose and there will be accident damage associated with the VIN which will bring down the value of the car, no matter who was at fault or what the circumstances of the damage might be. This is another reason I dislike car insurance companies.
I went through something similar to OP myself last year although the damage was not as bad as what OP has:
This is about my 2018 Nissan Rogue. Thanks for any help. I went to Lowe's today, when I came back out of the store I saw that one of their flat carts had either rolled on its own or someone did it but I got this dent in my left front fender now. I am looking for info/input/opinions on what to...
bobistheoilguy.com
My deductible is $500.00. The total bill for repair at the body shop was $921.00. I just paid the entire amount myself and kept the insurance out of it. I did the same thing when I got a rock chip in my front windshield earlier this year. My insurance would have "paid" for Safelite to fix it, but they also consider windshield repair a damage claim, it goes on your record, they can use it to jack your rates and it can detract from the value of the car with a damage claim on file. No thanks. I just paid Safelite myself and kept the insurance out of that one too.
The insurance company is not your friend. I hate to say that again but it is how I see it. If the total for this repair really is only in the $1,000.00 to $1,500.00 range if it were me I would just pay the bill myself and keep the insurance out of it.
I really hope this works out in OP's favor. Even more than that I hope they catch the dirtbag that hit OP's car and took off.