If you are certain that your own insurance will not cover the rental car, then no, you are not responsible for it; the other party's insurance company is. But for their insured hitting you, your car would not be in the shop and you would not have to rent a car at all and pay for the insurance to cover the vehicle. I assume you spoke with your own insurance company about whether or not they cover a rental car. I'm surprised, because most insurance companies do, except for certain fees the rental car company may tack on, like loss of use, and others. Be sure first, and then make your argument to the other party's insurer. Why should you be out of pocket that $29 a day if the accident was not your fault? You may need to have a car accident lawyer where you are (Ontario, California, I presume) make the argument for you.