I had a non-fault accident in CA a couple years back. I hit a couple loose dogs on a highway late one night. The insurance company will generally total a car in that type of shape.
When it happened to me, it was 2005 and i had a 98 accord V6 in perfect shape and 80k miles. I bought it from my mother and all records were immaculate. When the accident happened i had just put on new struts, cv boots, timing belt and the works as i expected the car to last another 100k. In short the car was worth more to me than KBB value.
The insurance process was quick and they evaluated the car in around a week and had an offer out pretty quick. This is how they get you. No Matter What, DO NOT ACCEPT FIRST OFFER. I was offered 7k for my car on first offer. I pulled all the local papers and website info i could, to find what i considered an exact match for my car (same miles, trim, upgrades, maintenance records, number of owners) and came to a price of 12k which was a bit inflated on my end.
After several weeks of arguing and proving my point with factual evidence, they gave me an offer of 11k and i accepted. And thus i purchased my 4runner.
Good luck, and remember the insurance company is out to make a buck, you are not their primary interest. The majority of people will not argue and provide factual data so hold your ground and make sure you are happy with the salvage value they provide. You insure a vehicle for replacement value, not what the INS company deems your vehicle is worth.
P.s. dont forget to list your upgrades and mods in your value. Even if you did the work. I even listed monies paid for maintenance, this was a contested point, but in the long run it helped as i couldnt find a replacement that had just had all that work done. Most cars they will counter you with are being sold as maintenance is coming due (timing, suspension, etc)
Oh and i had the caveman insurance.