Actually, Amex is self insured. Meaning they eat the expense every time they cover a loss.It's no different then telling your insurance company that your car got stolen, collecting for it, then selling it. It LEGALLY belongs to the INSURANCE CO to do with it what they want. Amex doesn't insure the phone, there is an insurance company that does it for them.
And yes, if the phone is recovered, it belongs to Amex.
To the OP, I am an employee with American Express (Lead Programmer), and I would love to hear more about your friends "loss". I don't work in the fraud division, but have many friends there who would love to read more.