The difference with fantasy football is that there are a few key stats that are considered very important in this simplified fantasy world, and thus earn points. These are minutes played, yellow/red cards, goals and assists for all players, goals conceded for defenders and goalkeepers, and saves made for goalkeepers. If you use those stats to select a team to play a game of real football (Moneyball style), I doubt your that team would do very well.
Of course - I won my EPL fantasy football mini-league this year with a midfield consisting of 5 wingers!
I think the major problems I have with the stats-based approach are twofold: 1)it doesn't account for tactics and team play- how a player is utilised in a formation and the players around him. If you play with Jan Koller as a striker you're gonna have way more successful longball attempts than if you play with Messi as a striker, to make just a really simple example. 2) it doesn't account for personality/psychology. players are assumed to play the same regardless of who they are playing with and for but that clearly isn't true. Some players respond better to certain coaches or environments than others do, take Shevchenko as an example here - compare him at Milan with him at Chelsea.
Baseball, like cricket, is a sport which is really more individuals playing in teams than a team sport - pitcher v batter/bowler v batsman - whereas in football, except in a few rare cases, it is hard to separate the statistical aspects of a players performance from team factors. Shots on target might depend on where your teammates are playing the ball to you for instance. Pass completion relies not just on your passing accuracy but on teammates to be in positions to pass to. Crosses completed depends on the aerial ability of your stikers. Successful dribble attempts might be the result of other players drawing defenders away from you with well-timed runs. And so on...
People like Coldplay and voted for the Nazis. You can't trust people.