Absolutely not. However, you must have your own insurance otherwise. A credit card's insurance is not the same and does not necessarily include personal injury protection. If you have an actual car insurance (for example State Farm, Geico, Allstate, Direct, etc...) then you can decline the insurance from the rental company. If you don't have car insurance then the rental company would likely refuse to give you a rental without paying for their insurance.
There is nothing illegal about a car rental agency refusing to give you a rental car if it is unrelated to your race, religion, or gender.
This is not to be considered legal advice nor does an attorney-client relationship exist.
The rental company can refuse to rent you a car if you don't meet its insurance requirements. They could also set very high standards for insurance--say, a million dollar combined single limits policy--but they would price themselves out of the market.
They are looking for liability insurance for your driving the car, usually associated with YOUR car insurance and not credit card protections. Generally, this is a matter of contract and they can make such provisions, leaving you to find a rental company that has different criteria if you disagree.
No but it will look to your insurance if there is an accident. It's always nice to have a second layer of insurance that is primary. Airing on the side of caution, if you have the money purchase it.
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