The resident attorney decided he should weigh in on this.
Here's the thing. A "reservation" for a car rental is, in essence, a contract. You agree to pay them, and so forth, and return the car undamaged and they agree to provide you a car.
If they overbook, that's is NYP (not your problem). The airlines have made special arrangements to limit the compensation they have to provide you, but those do NOT apply to rental car companies. if you have a confirmed reservation with a confirmation, they HAVE to give you a car.
If they don't have any cars, well, that may happen due to people extending their reservations and so forth. Simply insist that you want them to provide a car of at least size X (where X is what you reserved) at price Y (the price you reserved) and not a penny more. If that means they have to call up XYZ rental car company and rent a car from them in order to provide it to you, fine, that's what they have to do. In short, you simply insist, "We have a contract, I'll pay you and you provide a car. That's it."
If a company ever flatly refuses to do anything, simply call another company and pay them whatever they insist that you must pay, and bill your original company for the difference. This is your classic contract law damages -- the difference between the price you agreed on and the price you actually had to pay.
Hope this helps.
Regards,
Joe Hurley