I wonder how much of a role Bitcoin played as an impetus for finally coming out with this. Sure, it should have been done way before Bitcoin, but I bet that gave them a reason to put the peddle to the metal.
Visa's product is almost entirely orthogonal to Bitcoin. It has a fairly high service fee, which provides a (worthwhile) service of insuring both the customer and the merchant against misdoings by the other, that is, offering payments that can be reversed in the far future. It's centralized, and humans can reverse payments. It discriminates strongly on what fields they're willing to serve payments for. It requires not only identities but background checks of both customers and merchants, and can permanently shut down a customer or merchant they don't want to serve any more. It provides credit.
If they really felt threatened by Bitcoin, they would have changed any one of those things. Bitcoin doesn't even have an HTTP API, so adding one doesn't help you compete.