If the company continues to receive chargebacks claiming fraudulent charges (which this really does appear to be) they will find themselves in a difficult place with card processors.
Some processors drop clients if they crack 0.5% a chargeback rate.
The credit card processing chain is quite complicated, with banks, card companies, ISPSs, processors and merchants all having fairly clearly delineated roles. A merchant - no matter how big - implementing the whole chain is unheard of.
Visa, MC and other cc companies care a lot more about their reputation than they'll even care about a company like this.
Much larger fish have been put on the bbq over less substantiated claims of fraud.
As far as I know they use GE as the issuing bank, they may have other deals in place.
As far as I know - but this may very well be wrong or at least out of date - amazon does not have a banking license and the network used is VISA.
This seems to confirm that:
I would guess Amazon have looked at replacing as much of the payment chain as they can and done the parts that are profitable to replace. But they have a long way to go before the enormous hassle of becoming a bank is going to be attractive and possible.
Piss off VISA/MC/JCB/AMEX and you're in trouble.
Ultimately VISA determines who gets to participate in the VISA credit exchange network and will fine acquiring banks who participate in things like this. No one can force their way in and avoid responsibility -- period.