Having has to suffer for a time working for a company that had something of a scam going regarding employees and AmEx cards (Litton Industries, absorbed by Northrop-Grumman in 2001) I have some insight into how the story might have unfolded.
Litton Industries had AmEx cards issued to employees. It had your name on them, you were required to activate and use them, you were solely responsible for paying the balances, but the limit was set by AmEx based on Litton Industries' financial situation and thus were effectively unlimited. You were required to pay all company travel expenses with them (even charging airline tickets to them) and file for re-embursement when the trip ended (or monthly is it was long-term). Thus the employee could be on the hook for quite substantial amounts of money at the direction and for the benefit of the company.
Something like this could have happened to the poor employee.
But back to Litton Industries. They could not process a reimbursement claim (which required multiple sign-offs) within a week, it often took two (or even more). And they had a "payment cycle" that cut a check only once a month, if approval came in by the cut-off date. So if you took a one-week trip, filed immediately upon return, it was almost impossible to get the check in hand before the monthly bill was due, and thus you either had to pay the balance off out of your own personal funds, or you were hit with a late fee that the company would not reimburse for.
I did not stick around there for long.