Simply paying with AMEX does not automatically give you CDL insurance on your rental car. You have to purchase their rental car protection which costs $19.95 per rental, which is still much cheaper than what the car rental companies charge.
My DH learned this the hard way when his rental car was hit in a parking lot and we received a bill for $1200 from
Avis. He paid with AMEX and they would not cover it. He now has the rental car protection from AMEX.