Sports (especially football) are, inherently, a social phenomena. You need at least ten other individuals to comprise a football team (a QB "tweets" the play-call in the huddle). You need another team to play against (the NFL creates a Facebook "event", inviting teams to participate). Then, the true glory and excitement of a NFL football game is not achieved without the presence of thousands of screaming, die-hard fans cheering for the home team ("add friend", "Follow", "join group").
The social aspects surrounding the game are arguably more important than the game itself; tailgating outside the stadium or gathering at a friends house or a bar to watch a big game, hanging over the stadium arm rail to high-five your favorite player, the Monday-morning talk around the office water cooler...the weekly NFL football experience is all about people connecting on various social levels.
Banning social media only serves to stifle these social connections--between both and fans and between fans and more fans. By doing so, the NFL is (purposely?) limiting one of the best aspects of the sport.
Sure, the NFL is not at risk of going out of business. They make a tremendous amount of profit. They do not need to embrace or accept social media. This certainly does not mean that they should suppress it[or that they will even be able to...]