They didn't care. They didn't have to. Now they do, because they have to. (Hello, Google+)
Facebooks API docs are improving too - so this combination of quality docs and SO could be great.
I guess the point is, if you've spent a lot of time figuring something out, and you've proved that a number of solutions on the internet are now wrong, you're tempted to make it easier for the next guy. I think this is true regardless of the medium, but SO seems to have done well at creating an environment where it happens.
Since people are already discussing Facebook API over at Stackoverflow, they might as well make it official.
Why try and build your own community when there's already an existing one with a lot of useful questions, engaged moderators and smart people answering?
Especially when you've failed to support your existing community at all.
Community wiki posts can be outright edited by low rep users, and higher rep users can edit any post.
The idea that a wiki is better for rapidly changing content is... odd, to me; it seems it'd be a wash at best. Then again I'm an SE Inc. employee, so perhaps I just don't see the difference.
I think changing APIs is begging for a wiki much more than a Q&A site. Facebook used to have a wiki for their api, but they went and deleted it, which I considered basically unforgiveable and proceeded to do my best to avoid having to touch the API after that.
In short, bringing back http://wiki.developers.facebook.com/ and focusing on keeping it current would be a much better start than a Q&A site, even a really good Q&A site. You'd still have the need-to-keep-with-changes problem, but at least you'd have somewhere to start from, and wouldn't keep getting referred to out of date information when googling answers.
Yes I know Stack Overflow has community editable wiki question styles, but then you just compound the problem and now need to update 100 different 'how do I [x]' questions every time the API changes.