No, "Premium" Car Rental Protection is an extra cost feature available to purchase with any USA-issued American Express card. It is not "included" with Business Platinum. If you [Enroll] in this feature you will be billed for coverage each time you charge a car rental to the card.
Sorry, you are correct. It tells you to "Enroll" on the personal one when looking at the benefits. It does NOT say "enroll" when looking at the benefits page of the business card.