>>> which am I legally obligated ...?

I do not think you have to write them (the rental company) out a check for the loss of use. They'll try to put it on your card.

When you are charging your rental to a credit card with collision benefit and loss of use benefit, the crect card company might insist that the rental company produce car utilization logs and if the company does not cooperate, the credit card company might dispute the bill internally in your behalf and charge back the rental company for the loss of use amount they put through.

Initiate the dispute yourself with your credit card company if they do not do so themselves.

I think you are responsible for loss of use only for the time it should take to fix the car, not the time waiting for an appointment at the body shop.

Travel tips:
http://members.aol.com/ajaynejr/travel.htm