How will AmEx know that you used the miles earned by your card? If you earn half of your miles through your card and the other half through flying does it make a difference to them? Or does it have to be an award flight from your AP account that is linked to your AmEx?
They don't.
The rep just said that since I have an Amex AP card, they just assumed that I earned enough AP points to get a reward ticket and if I pay all the taxes and fees with my Amex AP card, they would just cover my trip.
There has been conflicting reports on the FT AC forum that Amex did or did not cover such reward tickets.