I will giggle uncontrollably as I note how utterly full of bunk that claim is. Going to offensive fWAR (or whatever ballpark normalized thing you like):
2014: LAA, Det led the league, Baltimore was 6th, Oakland 7th, Kansas City 10th
2013: Bos, Det, Oak, TB led, Cleveland 6th
2012: NY, Texas, Detroit, Oakland 2nd through 5th, Baltimore 11th
2011: Tex, NY, Det, TB 2 through 5th
2010: NY, TB, Min 3rd, Texas 7th
2009: NY 1st, LAA, Min, Bos 3rd through 5th
2008: Bos 2nd, NYY 6th, ChiSox 9th, LAA 10th
2007: NY 1st, Bos Cle 3th-4th, LAA 7th
So - excluding "regular season tiebreaker games" since 2007:
35 AL playoff teams ... exactly 4 playoffs teams were below the median (8th place or worse) in offense
25 of the playoff teams were in the top 5 in offense