Using "Declare a Story Detail" as a twist or "aha!" as a player:

Watching Person of Interest recently, there's quite a few times in the story where one of the detectives (usually Carter) finds herself in a compromising situation, only to reveal something that drastically changes how it goes - she's been recording the conversations, or she called in for backup before, or whatever.  Thinking about this from a Fate perspective, it seems like this is an excellent place for the use of a Fate Point, though I don't know if this type of thing is explicitly called out in the book or not.  

Is this common practice?  Have others done it?  Has it worked well?