Fakee big boss could have worked as an interesting "bonus" twist, one that came well after you beat the game and resolved the story. The problem is that it's presented to us as our "ending". As Alberto said, it doesn't re-contextualize anything, but it also doesn't provide any context for anything either. It doesn't really tie into the theme of revenge, it doesn't it tie into the theme of becoming a villain, and it certainly doesn't really tie in to the themes of words being a threat.
Therein lies my biggest problem with the game: it never, ever delves into its themes, something that, even in their dumbest moments, the other MGS games did. They talk about revenge a lot in this game, and then you never see the result of getting that revenge. They certainly achieve their revenge, but you never see how this affects anyone, big boss least of all. They were playing at it: Miller looks like he's going to snap and go paranoid on everyone, but it's never really fulfilled. His paranoia pays off: Huey is lying.
They talk about Big Boss becoming a "demon" a lot, and going to "hell", but Diamond Dogs is really a wonderful place with soldiers who act like 5 year olds and a commander who raises puppies and saves child soldiers. In fact, they subvert this even more by making Big Boss and Venom two different people, so this isn't even close to the game where you see Big Boss go evil.
There's also a lot of talk about the english language being a repressive power that dominates the world, but we never really see this other than in Skullface's rants. The game seems to agree with Skullface, given by the quote at the end of that mission, but other than that, there's no real fallout from preventing him from reaching his goal.