The Problem With DIPS

This is kind of a random topic today, but it's something that's been bugging me lately when thinking about sabermetrics, which I've been reading a lot about recently. Voros McCracken developed Defense Independent Pitching Statistics (DIPS) after concluding that the pitcher has no control over whether batted balls turn into outs or hits. His theory is that the only things that a pitcher has direct control over are his number of walks, strikeouts, and home runs allowed. He presents very compelling evidence to support that argument here (yes, I know the article is 7 years old), but there is one thing that I do not understand about it. If he argues that a pitcher has no control over a batted ball, then why are home runs a part of the DIPS formula? There is even a slight bit of defense involved in home runs, as a handful of home runs are robbed each year by excellent defensive plays. I assume this defensive component is statistically very insignificant, though, so I'm not actually worried about it. What I don't understand is why a batter gets credit for a line-drive double off the top of the wall with the pitcher supposedly having no control over it, while a pitcher is blamed for a hit just a few inches higher that results in a home run. To me, it seems like an arbitrary dividing point between what a pitcher controls about a batted ball and what he doesn't control. I am by no means an expert on the subject, but if the pitcher does not control what happens with a ball in play, how is it all of a sudden under his control if it goes over the wall? Obviously, the defensive impact on a home run is so statistically small that it can probably be ignored, while a ball in play is greatly affected by the defense. However, this theory seems to say that a pitcher has no control over what type of hit the batter has-- a lazy fly ball, a scorching line drive, or a slow roller in the infield-- so why would the pitcher be able to control whether the ball is a home run or not?

Maybe I'm misunderstanding this theory or maybe someone has done research on this that I don't know about, but this question was bugging me as I was on my way back from class today. If anyone can explain it to me, I'd like to understand why a pitcher controls home runs, but not any other type of batted ball.