They evidently disabled the AVS system which checks your cc payment info, i.e. alerts the merchant (Obama campaign in this instance) if card number matches name, address, or is an out of the country bank.
Without AVS, a person could use a stolen cc multiple times, or a person could use somebody else’s name for different cc’s. Contributions could be coming from out of the country, or as you said from prepaid cards, with no traceable information.
Foreign donors go through a world bank. Maybe the world bank is complicit in this too. They have to track all intl purchases and why can’t someone get their records?