Chase and Citi are very clear that their credit card coverage only applies if you decline the CDW from the rental company. Amex will apparently let you pay for a partial CDW from the rental car company, although I've never seen one of those in the US market.
For
Chase: "If you accept the collision damage waiver offered by the rental company, you will not be eligible for Auto Rental CDW."
For
Citibank: "We will cover you up to $50,000 toward the cost of repairs or the cash value of the car, whichever is less, if a covered accident or theft occurs when you pay for a rental car with your Citi card and/or ThankYouŽ Points
and decline the rental company’s collision loss/damage insurance."
For
Amex: "Coverage for Theft of or Damage to an eligible Rental Vehicle is activated when...You decline the full collision damage waiver (CDW) or similar option, or pay for a partial collision damage waiver, offered by the Rental Company"