Is Final Fantasy XIV the fastest turnaround ever on a so-called "exclusive?" I recall Assassin's Creed being very quick as well. We'll see how Conviction fares, but I suspect that the prospect of making more money with the same product might come into play.
When you create a product like an MMO, you don't begin your meetings with a discussion about how to limit your subscriber base. Reading comment threads, you'd get the impression that Square Enix didn't already have an MMO currently running on Microsoft's platform. I don't know that it made a particularly big splash, but in the contortions MS went through to get the game on their box, they broke system's cardinal rule: that players need a Gold tier account to play online. Indeed, they broke this rule so badly that eventually they had codify this sundered rule into policy. Not only can MMOs on the 360 allow online play from Silver accounts, they can also require storage - the two things no title is supposed to do. There's no barrier for Square or Enix on the system - at least, no barrier they haven't already agreed to.
With their own cross-platform engine, there's nothing to stop Square Enix from releasing the game anywhere they damn well please. This isn't the first time they've played the platform holders off of one another, and it won't be the last.