I can't imagine how anyone can think it wasn't a good idea for SE, on so many levels.
First, this game is likely to top off between 1.5 to 2 million on the Xbox. Those numbers alone are impressive, especially for a JRPG on the Xbox. Considering that it was a port of a game they already made, using a cross platform engine, it couldn't have been too expensive to make either. Even cheaper if there were money hats from MS.
Second, exclusive advertising. Pachter recently pointed out that marketing is something half the budget of a game, and MS footed a huge part of that in the west, which is arguably the region it needed it the most. They could rely on the hardcore fanbase to know it was coming for the PS3 (they've been hyped for 5 years), so salewise what's most important is getting the word out to the Xbox fanbase who may not have otherwise bought the game. Besides, the brand association between the FF franchise and the Playstation is still super strong, so just having large numbers of FFXIII ads running (even those showing only a 360 logo at the end) would benefit both versions (seriously, it takes one second to google this info, or I don't know, see it with your own eyes in the store). And lets talk about a theoretical gamer (since we're all about this "what if" thing). Gamer A owns a 360 and PS3. He sees a commercial for FFXIII with the 360 advertisement. He says "wow, I haven't played Final Fantasy in years. I should check that out". In the process, he discovers that the PS3 version is better. PS3 version just sold one more copy. How is this not a great deal for SE (and for that matter Sony and MS)? SE gets free ads and the opportunity to grow a new fanbase, Sony gets their biggest rival to advertise a game that'll sell better on their system, and MS just made FF into a multiplat franchise and sold a bunch of games.
It's a good measure of what numbers SE can shoot for on the Xbox in the future, and it cost them very little money and risk with a good chance they'd make a lot of money. FFvXIII may or may not stay exclusive (I'd personally lean towards it being the same deal as FFXIII), but FFXV and XVI and so on sure as hell won't. This is a sizable market for SE, one that wasn't available to them before, one that has the potential to grow into something bigger. It's simple economics. I was selling 100 things in America and it was great. But hey, China wants to buy 60 of the same stuff. Great, I'm now selling 160 things, making more money, and growing a new market.
To point out two specific instances, I'd like to bring up the launch month NPD sales for FFXIII. FFXIII on PS3 sold about as much as FFXII did back when it launched. Great sales, considering the smaller userbase. A good indication that the franchise loyalists will go where the game is, and how much they were hyped for it. But the 360 version sold 500,000 copies as well (roughly 1/3 of the sales). Thanks to the 360 version, FFXIII outperformed it's predecessor by 50%. Now ask yourselves, would FFXIII, as a PS3 exclusive, have sold 1.4 million copies in the US in it's launch month? Would it have outperformed FFXII by 50%? Likely not.
In the UK, chart-track has shown that so far, the 360 version has had better legs, and the two launched very closely to each other. We don't have hard numbers, but it seems likely that the two version are essentially tied now, and possibly even selling better on the 360.
Those are two regional examples we have of rosy sales for the 360 version (in the 1st and 3rd largest individual game markets, no less). It doesn't change the fact that in the west, the PS3 sold considerably better, but the 360 version never needed to outsell the PS3 version to justify it's existence to SE, it just had to sell great on it's own merits. It has done that. It represents 40% of western sales.
Those are the reasons I believe that SE is happy with their decision. Feel free to disagree, but I'd appreciate it if anyone can list specific parts of the argument I made to disagree with. I enjoy a good debate.