I agree with your completely @EAMann and sorry to differ @tnorthcutt. I don't think it's a problem if we send them to Google first because it we follow a somewhat aggressive policy of policing really high quality answers then over time (and not too long a time) this site will be one of the top search results for practically every WordPress related question. And if my experience with Googled questions leading to StackOverflow is any experience, we'll also have the best and most relevant answers too. So if we focus on creating really quality it will be rewarded.
So yes, I think the FAQ should seriously discourage people from answering their own questions and that if they do we should close the question (can we delete them?)
In the case they do identify the answer on their own we should require the ONLY do so in the comments after their question and further they should encourage and accept others to answer it more completely for others who many have the same question in the future.
On the surface I like the idea of a waiting period but it might encourage hit-and-run questions where the user never follows up to close the loop. But if the time period is reasonable it might make sense. At least be worth a try.
I would like to add (maybe this should be another topic of discussion) that our FAQ state that by asking the question the commit to following up and closing the loop to make sure the answer has as much value for others in the future as it did for them and if they can't commit to doing and they show evidence of not following up they will be notified and possibly banned (for example, without calling anyone out I noticed there is someone who has asked 5 questions recently but hasn't followed up on any of them.)