The Facts:

Exhibit A: "Nine of the 29 batters Greinke has hit in his career have been Sox hitters."
Exhibit B: "Greinke has hit four Oakland Athletics -- second most but still five fewer than the White Sox."
Exhibit C: "There also have been some near-misses, such as fastballs that buzzed the heads of Carlos Quentin on April 8 and Alexei Ramirez on May 3."

Quotes from

1. Dye: "He knows he has to keep us honest and pitch in. "
2. Guillen: "[Greinke] is a great pitcher and I don't think he's going to hit people just because he wants to hit people."

Conclusion

He's inside their heads. They're more worried about him than hitting the ball.

Prediction: The Royals win 3-1. The Sox's only run comes from a Dye homerun