rental cars use leasing agreement nowadays. When a car sustains damage in the undercarriage (and they are very specific about it), the car is yours, you cannot turn it back to the car company. a company like avis/Cendant will buy 40,000 cars and not even blink per month. Those cars are "leased" under specific programs with GM and other manufacturers. After a certain amount of time, and a certain amount of miles, the car is eligible for "turn back" to the manufacturer. If the car exceeds that mileage, or exceeds that time, the car is yours and the full price of the car is charged to you.

At turn back, an inspection is done. 99% of the time that cars are rejected, (other than too many miles or too long) the cars are turned back due to undercarriage damage, from off road driving. This is the primary reason they do not want you going off road. Sure its safe if you go slow but if you bottom out once, and bend the wrong part (even if the car operates properly) the car is theirs and they must liquidate it through auto auction yards (and up until recently, car dealerships owned by the rental company).

Technically, if the car was inspected and the rover agent upon checkin spotted the undercarriage damage, you would be responsible for the damage to repair the car. However they do not have the time or the means to jack up every car and inspect for off road damage.