I am not sure about other rental companies but it is important to understand that although referred to as
insurance, it isn’t really insurance at all – rather, the so called insurance arrangements are terms of your contract with the rental car company. The rental car company itself may be backed by its own insurers but this insurance cover, if it exists,does not extend directly to you.The protection you obtain from the rental contract is only as good as the ability of the rental car company to meet any claim. If the rental car company has few assets, in some circumstances that may leave you as the driver of the vehicle open to liability to third parties.It is a good idea to hire vehicles only from rental car companies that are obviously financially sound, and are more likely to be able to honor the insurance provisions of their contracts.
We have always tried to rent from Hertz while on the island as they include the liability damage waiver in their rates and we take the CDW/LDW from one of our credit cards.