Imagine this:
You are the Linebacker responsible for covering Vrable on a goal-line play. You are also responsible for outside contain on that run play. On the goal line you play the run first, no matter what. Vrabel comes up, and gets into you a little bit so you push back. As a defender, the play feels like a run.
As Brady has said before, the O-Line has as much to do with this as Vrabel. Anyone who has played football can probably tell you if its run or pass in the first 2 seconds of any play depending on what the lineman do.
So, as the linebacker, the lineman are run blocking. Vrabel is coming up to block you. You take on Vrabel as a blocker. Except a split second later Vrabel gives you the swim move and he is past you. He is past you because your momentum is towards the offensive backfield and he is going the other way. You cannot change directions fast enough. He is behind you, and in the NFL all it takes is .5 seconds of being open to make the difference between a TD and an INT or incomplete.
In short, the entire offense fakes the run. The O-Line, the QB, the RBs, and Vrabel. The linebacker bites on the run and Vrabel is wide open.
As to why the defenses don't key in on it? Do you really think this offense only does one thing with a specific personnel package? No. They run (probably more often, I don't have stats or game film) with Vrabel in there also. That is why that fake works.