During the last year I was unable to find a foreign bank, including U.K., Switzerland, Russia, New Zealand that could send money to a US VISA card. I contacted VISA on the issue, but they replied that I need to contact the bank that had issued the card. After I replied that the question is about any US bank that issued a VISA card, i.e. VISA itself - they sent me another answer that I did need to contact a particular bank (this time a template for those, who do not understand from the first message).
Thus it looks like VISA e-mail is machine read and one cannot get past this barrier. Many world banks allow topping up a VISA card, issued in most countries, for $4 and even $2. Thus you are able to pay credit card bill from almost anywhere in the world, including thru card to card transfer. So MasterCard looks like clearly a better choice.