Renting is different. It has to do with covering the rental compnay for loss of their rental on that car if it is out of service. You actually dont have to buy their insurance. Typically your insurance and your visa coverage will be enough to cover a rental.
I got a ticket a few years ago for lack of proof of insurance. I had insurance, just misplaced the card. I got a letter from the insurance company stating the vehicle was covered at that time. The judge made me get another letter because my name wasnt on the first one. My agent was mad- the car was covered, doesnt matter who's name it is in ( it was in my husbands name).
eta: some people do carry umbrella policies. It covers them no matter what they are driving. Typically people who own multiple cars carry that type coverage, and its not that common.