You obviously don't have a debit card. It's not "a permutation" of a credit card and they don't come from visa or MasterCard. You're talking about a credit line through your bank. I own a debit card. From my bank. With only my bank as the issuer. It takes money directly from my bank account when I use it. No creditor involved. It's a money transfer straight from my bank account to the retailer I use it at. Millions of people have them.