Go ahead and sort any team's regulars by BA and then check the correlation to OPS.
Look at the Sox:
Top 2 in BA - Yoshida .300, Verdugo .286
Top 2 in OPS - Yoshida .842, Verdugo .801
Bottom 2 in BA - Casas .201, Kike .231
Bottom 2 in OPS - Kike .661, Casas .697
So you have one small non-correlation. And these aren't isolated examples.
TTO Kings like Schwarber aren't really all that common.