The logic pretzels that are used to unravel and define the phrase "most valuable" are twisted -- so much so that, in the end, the conclusions are often completely illogical. It is through this strained effort that Mickey Cochrane won the American League MVP Award in 1934, after a fine season in which he hit .320 with 2 home runs and 74 RBIs, while Lou Gehrig finished fifth after winning the Triple Crown with a .363 average, 49 home runs and 166 RBIs.
The criterion for MVP doesn't indicate anything about granting additional favor to the best player on the best team, and we know this because Cal Ripken, Alex Rodriguez, Ernie Banks, Andre Dawson and others have won the honor while playing well for bad teams.