Sorry to revive an old thread, but I was wondering this exact same thing. When you go to add a payment method on your EC profile, this message comes up:
Credit cards on this profile must be in the same name as the Emerald Club member.
National Car Rental does not accept debit cards at the time of rental. Saving debit card information in your profile may cause your rental to be cancelled or voided.
So I guess they've thought of someone just adding a debit visa onto their profile, only to have the system not recognize it at checkout.