My reasoning.....There are so few games in the NFL season, no one can afford to play like they know they don't have a snowballs chance in hell. Every game is important, especially when you play only once a week.
Baseball, basketball, hockey.... now they could since they have so many games. But in football, one loss hurts. The Giants wanted it that much more than the Skins did. They got outplayed on both sides of the ball and I believe the Giants will be a much better team for it.
My theory is impossible to prove, but for me it's the best explanation that fits the facts. The skins are a much much better team than that.