I am not sure I understand about this business of a Credit Card 'contract'. I have had my Visa & Mastercards since 1986 and have used one or the other to pay for holiday expenses, including car rental. I also have a very comprehensive travel and dive insurance with my bank that covers me up to 40 metres and all my luggage and dive kit. I had no problems when I had to make a couple of claims over the years - one a last minute cancellation due to the wife being unwell and another due to lost luggage (but in the latter case the bag was found and returned to us intact weeks later and so I returned the reimbursement).
But as far as Car Rental abroad goes, the insurance company made it clear that they just covered me (injuries) and my luggage and not the rental car. I have therefore always upgraded to the full insurance offered by the car rental company. I visit and drive in the USA quite often and usually use Enterprise or National car rentals and add their full cover and fuel surcharge every time. Thankfully, never had to make a claim thus far.
What my question really was - if I buy AB's full insurance (which I now have done), is the coverage as comprehensive as renting a car in the US? I asked because this will be the first time that I am renting a car in the Caribbean.