Legally a driver only needs to have liability insurance. The insurance only pays damages of other people's car when the insured caused an accident. The insured driver gets nothing for the damage to his own car.
When this driver causes an accident in rental car, the insurance only pays damages of other cars, but not the damages to the rental car because this driver was at fault. In this situation this driver should have bought insurance from the rental car company.
However, if on top of liability insurance, a driver purchased collision (due to accident) and comprehensive (due to crime or disaster) insurance on his own, he/she does not need to purchase additional insurance from the rental company.
