The fact is that the contact with Schweinsteiger's hand changed the direction of the ball. Evra had flicked it on to somewhere in front of goal - who knows - it looked like it was going somewhere near the penalty spot. Once the German player's hand contacted it, it went the other direction. I think the AAR had the ideal angle to see the play.
NONE of the laws are clear in the way they stand. it's the substantial "jurisprudence" of official circulars and recommendations, accompanied in seminars by hundreds of concrete illustrations, that make them so, and 12 has been made one of the clearest... to real referees and fans of course, not to armchair geniuses. "hand-to-ball" in english, "décollée du corps" in french are part of the shorthand one hears that aren't, perhaps never were, official language, and sometimes obfuscate public perception. here it doesn't matter if schweinsteiger saw the ball coming or if he moved it towards the ball deliberately. all that matters is that he's put his hand where it doesn't belong. other guidelines like distance or arm movement are for cases where a player's arm is in a position one can expect. you're not required to play in the box with your arms behind your back* but if you touch the ball with them in a normal running position you leave yourself open to the ref deciding you had the opportunity to get them out of the way in time. *observe closely and you'll see that often a player with his hands behind his back has his elbows extended as far as possible - never underestimate the slyness of the professional footballer.
This is, to put it simply, a brilliant and logical way to look at it. So much better than unnatural position.