More Rewards was launched as a benefit of, and is currently limited to use by, Chase Rapid Rewards Visa cardholders. While I'm not privy to the details of the marketing agreement between Southwest and Chase, since More Rewards is limited to Chase customers only, presumably Chase is paying for the items, at least partially (if not in full).

As I listed above, Chase is currently advertising More Rewards as a benefit of their card membership. If actively doing this while aware that the program is gone for good, they are in fact committing false advertising.