The discussion is about these words:

"You are covered when Your name is embossed on an eligible card issued in the United States, and You use Your credit card Account and/ or rewards programs associated with Your Account to initiate and complete Your entire car rental transaction. Only You, as the primary renter of the vehicle, and any additional drivers permitted by the Rental Car Agreement are covered."

flycar did not use the Chase card to initiate the transaction. The customer cannot choose the card with the best insurance after the car was damaged, but that's apparently what happened in this instance.