First off, that is retarded in and of itself. You don't just remove 40 homerun, 1.000 OPS guys, replace them with Rey Sanchez and not suffer in the lineup. Argument is flawed off the bat, incredibly. Yankees would suffer just as much as (if not more than)the Sox would.
In baseball, value can only be definied by individual stats, which I'll get into in a little while. A player's value in baseball is his defense, his offense and to a much lesser extent, his 'intangibles'. Now in this case, Rodriguez has brought very good defense (top 3 in the league). Ortiz has brought no defensive value. Which means Ortiz has helped his team win 0 games in the field, and Rodriguez has helped win at least a few. (yes, games can be won or lost with fielding. The team that trades Garciaparra's offensive prowess for Doug M. and Cabrera should know that.) Next is their offensive statistics. Rodriguez is better in Average (which I don't put stock into anyway), and more importantly OPS and OBP, percentages of a hitter's success each plate appearance. These two stats are widely recognized as the most important tool to judge a hitter, because they judge success vs. opportunites. Again, advantage Rodriguez. Intangibles (clutchness, etc.) is hard to define, but hits in big spots do count for something, as does leadership. However, to think a homerun in the 3rd inning is worth less than in the 8th inning is just not smart. RBIs are RBIs, homeruns are homeruns. No matter where they come from, they help your team win. And while I absolutely give Ortiz the advantage in this category, it certainly does not make up for the discrepencies in the other sections to qualify him for MVP.
Would you people get together and make up your mind.
Anyway..
A player's value is not determined by the rest of the team, or their standing. Suppose you have a player, who plays gold glove defense at short, hits 1.000 for the year with 525 homeruns in 525 at bats. Also suppose, that his team is absolutely terrible around him. His pitching staff gives up more runs than he puts on the board, and they go 0-162 for the season. Suppose a guy on a first place team hits .300 with 35 homers and 110 RBIs, best hitter on their team. Is the guy who is on the first place team more valuable because of their standing? I don't know, but it seems the guy with the better statistics was a bit more important to his team. Any way you slice it, the player on the 0-162 team had more value.
You can't penalize (or reward) a player for being on a good team. This isn't basketball or football, where if a guy puts up big numbers, success is guaranteed to follow for a team. You have a QB with Peyton's season last year, you are definitely winning some games. Put vintage Jordan on a bad basketball team, they make the playoffs. Vintage Gretzky would take even the NY Rangers to the playoffs. Baseball, you put Babe Ruth on the Royals, they're still in last place.
A player being valuable (most valuable) is not contingent upon his team's success, although they often do coincide.