as far as i know, when it comes to a stolen recovered car, you can refuse to have it back, for the reasons stated above, and also the fact that your not going to be happy with it, as alot of work will be involved
also if you do keep the car and they repair it, it wont be listed stolen recovered, shouldnt go under any cat e.g cat d etc...
glad you've got the car back, but its a real pity about whats happened, some one really needs to put a stop to these car jackings