You're correct that the original story said these were debit cards, not credit cards.
I don't see how this necessarily requires Mastercard's approval. Presumably "a major international bank" (MIB) can already issue Mastercards, and guarantees them. Do Mastercard themselves approve every type of Mastercard that MIB issues?
MIB could come to a private arrangement with BitInstant, that goes like this: BitInstant maintains your balance. You use your BitInstant/Mastercard/MIB debit card. MIB credits the vendor and debits BitInstant. BitInstant debits your account, converts it to "real" money (that's what they do) and credits MIB.
If Mastercard is already happy with MIB issuing Mastercards, and MIB is happy with its arrangement with BitInstant, then what's to stop this going ahead? The danger to the end user is that BitInstant goes south and loses your money, but that's not Mastercard's or MIB's problem, except MIB would be liable (I expect) for the payments it had accepted (and guaranteed), but not yet been credited for by BitInstant. As far as Mastercard are concerned, it would be MIB that backs any and all the guarantees that you get with a Mastercard.