I was explaining to my girlfriend why guillen tagging from second to get to third while someone is trying to score while the catch is the second out is dumb, because if guillen is thrown out it could negate the run (that was not the first time I have seen him do it, and has been a close play on multiple occasions).
It's not a dumb play a few of the times Guillen has done it. What he is trying to do is draw the cutoff throw from the OF in order to allow the runner from 3B to score without a play. He wants to try and draw the play to him, either make it to 3B on his own or get in a rundown long enough to let the run score. Early in a game, it is questionable. But I can recall clearly a time when he did it late in the game allowing the tying run (Byrd) to score. My immediate reaction was the same as yours but after watching the 3B coach and Byrd both acknowledge Guillen with 'atta boys' I got what was happening out there.
In many circumstances, it is not the optimum strategy, but if you are playing for that one run (which the Nats tend to do), it makes sense.