No, it doesn't add up like that. It's concurrent.
I believe that you're the one who might be incorrect. Prior to purchasing my rmbp, I did some research online and there were multiple examples where people utilized the amex extended warranty within the year after any purchased extended applecare expired. This is also stated in the terms for my card. In fact, that is one of the reasons why I purchased my rmbp using an amex card.
To make sure that the amex policies have not changed I went to:
http://www.americanexpress.com/us/content/card-benefits/extended-warranty-terms.html
It may very well depend on your specific amex card but for mine here is the specific policy:
DESCRIPTION OF BENEFITS
Where a Loss has occurred during this Plan's extended warranty time period of up to one (1) additional year, We will provide a benefit equal to the coverage of the original manufacturer's warranty on warranties of up to five (5) years. We will pay up to the actual amount charged to Your Account for the product for which a Loss is claimed, but not to exceed $10,000.
If the product also is covered by a purchased service contract, this Plan’s extended warranty time period begins at the end of the service contract and extends the original manufacturer’s warranty for a period of time equal to that warranty, up to one (1) additional year. If the combined coverage of the original manufacturer’s warranty and the purchased service contract exceed five (5) years, the product purchased is not eligible under this Plan and no coverage applies.
Based on the above policy, Amex should provide an additional 1 year coverage beyond applecare so you should have a total of 4 years (year 1- original coverage, years 2-3 - extended applecare, year 4-amex extended warranty).