This is what worries me. Are you 100% sure you didn't sign a form when you picked up the courtesy car? And if you did, are you sure it doesn't say that you accept liability for the costs?
Ignoring all that, you have a legal responsibility to minimise costs anyway, so if it's not sorted soon you need to be looking to get a cheaper loaner. Still via the AMC, but you do have to do it or this is going to come back and bite you. Plus there's the moral side of it, by increasing costs all you do is push up everyone else's insurance (including your own) too.