Since this morning, they added another sentence to the credit card section:
All Rapid Rewards Credit Cardmembers and up to eight additional Passengers traveling on the same reservation are eligible to receive a credit for their first standard checked bag. The cost of the first standard checked bag will be refunded to the original form of payment used to purchase the bag. Customers can use any credit card for payment to qualify for the refund, including but not limited to the Rapid Rewards Credit Card. Customers do not need to call their bank to issue or receive their refund. The refund will be processed by Southwest.
Cardmembers who are already exempt from other checked baggage service charges will not receive a credit for an additional standard checked bag.
So, I'd say that's the definitive answer that status or credit card only gets you the first bag, no stacking. Or, if you're getting a business select seat that comes with two bags each, the credit card doesn't get you a third one.