Are the tickets all on the same reservation? I know people have reported them waiving it on separate tickets, but not sure if that involved just one companion or multiple. The T&C's technically require all tickets to be in the same reservation. I'm not sure where you see that the ticket must be purchased with card. As mentioned above, that is not a requirement and I certainly don't see it anywhere.
http://www.delta.com/content/www/en_...-bag-free.html