Amex push the chargebacks/disputes back to the retailer who accepted the payment from someone using a stolen card. The retailer then has to prove the transaction was genuine to keep the funds (assuming they didn’t refund before the goods were sent or services rendered) - this is usually not possible, so Amex get the money back and the retailer loses out.

Amex’s only cost will be the time spent dealing with fraud reports over the phone, and money spent issuing and dispatching new cards to customers affected.