Amex offers 1 extra year of warranty coverage beyond what the store/manufacturer offer. So after your warranty ends, and you're within that extra 1 year with Amex, they'll reimburse you the cost of the item. Many Amex cards, the ones with better benefits, charge you an annual fee to use. Hence, the reimbursement you get from your item can offset the fees.

Amex has additional 1-warranty for your purchases. So instead of buying a new phone (since the manufacturers warranty ended), he is getting a replacement phone for free from Amex. Just that one event is paying back for the fees occurred in the previous years.