Here's his full policy as stated on his website: http://www.daveramsey.com/etc/cms/debit_card_policy_32.htmlc

Note the bit at the bottom about not actually being able to tell a debit card from a credit card. This is really just a philosophical position. He can't enforce it online due to how the card processors work. I believe he tries to enforce it at his live shows, though, by simply not taking any cards that appear to obviously be credit-only.