Sorry to see this.
The following applies to you and anybody who is involved in an accident and needs to work with an insurance company:
I had a really interesting (and long) discussion with a body shop owner in Washington a year or two ago regarding accidents and insurance and claims. I'll have to research hard who this was, though I called him for a PPI on a car I was looking at, and he was so forthcoming, I could no longer consider the car I was interested, specifically due to his findings. He was referred to me by the lot selling the car too, almost funny.
Essentially what he was saying, in cases like yours, you would refuse to accept the claim and tell the insurance company you are going to sue them for damages, loss of use, and legal fees. Seemed like a bit of a scam, but the guy, (Jeff it turns out-see below) said it's the way to go. Not having a wrecked car, I didn't have to give it a go.
OK - I did some looking and determined I spoke to Jeff at Haury's Lake City Collision in Lake City, Washington. Attached is the link to the yelp review which mention both positive and negative results of his methods.
http://www.yelp.com/biz/haurys-lake-...lision-seattle
I do think he'd give you the same information about the method, if you were to call, and he had available time. I wouldn't tell him you are in Tennessee, (and you'd want to be sure of the local laws), but I would call him and ask him to detail how he does this. If nothing else it would be an interesting conversation. My conversation with him has stuck in my head, and was the first thing I thought of when I read this post.