My understanding of the Amex baggage allowance is that it extends to anybody who HAS a Delta Amex card - nothing to do with paying for the ticket:
http://www.delta.com/content/www/en_...p/checked.html
Half way down..
DELTA SKYMILES CREDIT CARD FROM AMERICAN EXPRESS BAGGAGE BENEFIT
At the time of check in with Delta for a Delta-marketed and Delta-operated flight (including Delta Connection), our passengers who
hold a Delta SkyMiles Credit Card from American Express - Gold, Platinum, or Reserve - will be allowed to check their first bag for free system wide. The benefit is subject to the weight and size restrictions of your cabin of travel. The benefit extends to up to 8 travel companions on the Cardholder's reservation for a total of 9 passengers.
But as Widget mentioned, according to their
T&Cs it's supposed to be for the primary card holder only - not additional card members.
But I know that several secondary card holders under my account have used their DL Amex card and get the free bag. I've seen plenty of people at the counter just waive a DL Amex card to get free bag (no idea whether it's their card, or just borrowing a friends?)