buccourt - Unfortunately I had to deal with insurance companies in the past. This was in 2001, I was rear ended and my already "oregon reconstructed" title bmw was totaled again. They called and told me the amount they will pay, title brand was never mentioned before or after the transaction. I was more than happy with the amount, it was slightly on the higher end market value regardless of title.
However, my friend had a rebuilt title car, and it got hit, insurance only offered him half value. He did not fight it and figured they had the authority to make that call. I would have fought it, because I also know from my own experience and others, it is common for insurance companies to low ball or deny claims all together the first time. As a matter of fact, I heard it from insurance experts, it is part of their job to low ball and deny first (this is how they make more money). They know, a certain percent of people will not put up a fight thinking thats just the way things are or it is a hassle to challenge the insurance company. But, you don't go to court, most of it can be handled over the phone.
So, ask them how much they will give you first. If you don't like it, tell them your price and stick to it. It might take a few tries till they agree.
Every situation is different. And remember, even though insurance is more computerized now, they still have humans who can over write many parts of the process. If you fight back and they see it as a potential time waster for them, they won't waste their time and will often be more lenient.