Of course the FA are investigating him, this isn't a case of bias against Liverpool, or corruption of Webb. Babel questioned the integrity of a referee, you simply can't do that as a player, it's bitter, and it brings the game into disrepute.
If Webb really tries to help Manchester United, he doesn't do a very good job of it - this season in the Premier League at Old Trafford he made two decisions which directly lead to goals for Liverpool, in 2008 he sent Vidic off in a game Liverpool won against Manchester United early in the season. Also, today, if he was biased he had several opportunities to award more penalties for United if he wanted to make sure they won, but he didn't, because he is an honest referee and he didn't think they were penalties. That's not to say he's a good referee though.