subject: U-Haul Truck Accidents [print this page] 3. Rental Company Offered Insurance There are different types of coverages that are offered by the rental company at the time of picking up the vehicle. Many of them are simply damage waivers relieving the renter of the responsibility for repair of damages to the rented vehicle that occur while in their possession. As with the personal auto policy, all too often the renter does not understand the need and available coverage. The decision on these coverages can be one of cost rather than risk.