Not true, they can write the car off exactly the same as your own insurer can sadly. Look at it this way: If the TPI (third party insurer) wants to write it off but you don't agree, then you go through your own insurer and ask them to repair and claim back costs. They look at it, then agree with the TPI that it's a write off financially, so you're back to square one and it's in every insurance contract that you agree to let your insurer handle each claim as they see fit.
The only alternative you have is to cancel the claim completely and repair yourself. Sometimes this can work out for the best, especially if the car is worth peanuts or you don't want to lose NCB (although you still have to declare the accident regardless), but I don't think that's a realistic case here.