I called AMEX.
The customer service rep explained that the statement closing date can be whenever they want and will vary from month to month.
She said the some cardholders have the privilege of "paying over time" for some purchases over $100. For those that have this privilege (which I do) AND have qualified purchases during the cycle, the due date will be (in my case) the 21st of following month, regardless of when the statement cycles. For those who don't have that privilege, the payment due date will be (in my case) the 11th of the following month.
For those with the pay over time privilege - 25 days to pay.
For those without the privilege - 15 days to pay.
BUT (a big but here) as long as the payment is received and acknowledged my AMEX prior to the statement cycle close, the payment will not be considered late.
For my particular case, I had qualifying purchases, but since I pay as I go (for the most part) I had already paid off the purchases and had a small balance due when the statement cycle ended. I had actually missed paying it off by a few hours. Dang it! And the next charge (which would have qualified for the pay over time) hit my card on the 26th. Normally, that would have made my due date the 21st of the following month.
Oh well, learned something new! 
