Simple question: Does the resurgence win you the division, nevermind winning it all, but the division, without the 3 pickups? According to you, that was the bigger factor in their improvement, and they improved by 14 games from 2008 to 2009 (89 wins to 103 wins). According to the numbers, your answer should be "yes", because even a 50/50 split for the two factors gets them to 96 wins, one more than the Sox. You'd have a hard time convincing me that you would win the division without those 3 players, though.
I agree with you about the importance of having your pitchers go deep into games, but you conveniently don't consider that 2/3 of those pitchers were part of the 3 big additions. Yeah, having current roster players perform better helped, but the big, dynamic change was the 3 additions, and it isn't particularly close, IMO.