Last night while listening to the radio broadcast of the Phillies/Mets game, I heard Larry Andersen bemoaning the Phillies inability to win against the Mets this year. (Of course, he was talking when it looked like the Phillies were going to drop to 1-5 against the Mets this season and before the Phillies tied the game up in the seventh and took the lead in the eleventh.) A large part of his reasoning was that the Mets are the Phillies' chief rival in the NL East right now and a team can't win its division without doing well against the chief rival.
On the surface, Andersen's comments ring true to an extent. It's certainly not necessary to dominate your chief rival, as the Phillies did last year against the Braves, winning 14 of 18. But, a significantly losing record against your chief rival will hurt as each loss is a two game swing in the standings. Take last night's Phillies win for example. The Phillies entered the game 2 games up on the Mets. Had they lost, they would drop to only 1 game up. However, the Phillies won, so they are now 3 games up on the Mets. Andersen is absolutely correct that winning against your chief rival is important in this sense.
However, he's wrong as a historical matter that it's necessary to win against your chief rival. In fact, he's shockingly forgetting last year. Last year, the Phillies won the NL East by 3 games over the Mets, yet they lost the season series to the Mets -- 7 Phillies wins, 11 Mets wins. Losing to their chief rival certainly didn't stop the Phillies last year. Of course, their trip to the post-season would have been easier had they finished with a winning or even .500 record against the Mets. But, they didn't need to win against the Mets to win the NL East.
And that's held true for many recent playoff teams. Looking back over the last 5 years in the majors, 11 of the 30 division winners have had losing records against the division runner-up. Interestingly, the worst record during that timeframe is the Phillies' 7-11 record against the Mets last year, but there are also a lot of 8-10 and 8-11 records.
Of course, having a winning record against the runner-up is certainly preferable. But, despite Andersen's concerns last night, it's not required.