Had a very similar accident once. The guy behind tried to weasel out (to the point of coming up with a lying "witness"), but considering that it was the rear end of my car that was the worst off and I had taken photographs of the scene with my mobile, it didn't work.
Apart from the agrivation and delay, the problem was that they decided that my car would cost more to repair than it was worth, so the insurance only paid out the trade in value of my car. Which was considerably less than the cost of a replacement. And I had the FUN of going car shopping, when I didn't have a vehicle to get to a car shop.
Apart from the agrivation and delay, the problem was that they decided that my car would cost more to repair than it was worth, so the insurance only paid out the trade in value of my car. Which was considerably less than the cost of a replacement. And I had the FUN of going car shopping, when I didn't have a vehicle to get to a car shop.