Hobbies and Crafts Does the Costco Visa credit card have travel insurance? Does Costco Rental Car primary insurance? The Costco Credit Card rental car insurance covers rentals worldwide – and outside of the U.S., it's considered primary insurance, which means it covers the car before any other insurance policy takes effect. Related Posts:Does Costco have financing for furniture?What type of insurance does Costco have?The complete list of Comenity Bank credit cards can be found on the official Login page.Do Hertz accept cash?