I know it's easy to cheat. Don't do it or Jon Rauch will hunt you down. And probably shank you.
The 1996 Minnesota Twins didn't have much pitching. While they didn't have much power from their offense, either, their .288 team batting average trailed only the Cleveland Indians (.293). Additionally, their .357 on-base percentage was seventh in all of baseball.
They also led the Majors in double plays. But that's touching a little close to home.
Of the nine position players on that '96 club that received more than 300 plate appearances, seven of them had on-base percentages higher than .360. But who was the only one of those seven unable to crack the .370 mark?