Why the holy flaming buttery hell does that count against you as a baserunner? Makes no sense. Baserunning is about what you do once on, the mad scramble for first base after you've put the ball on the ground has zero to do with skill and even less to do with baserunning.
Double plays are about contact and quality of contact. They're a natural drawback of highly skilled contact hitters. The harder and more consistently you hit the ball the more you will hit into double plays. it's not what you want to be doing, but if you're HIDPing a lot, it's because you're putting the bat on the ball and getting it fair, and getting it to the fielders quickly -- if you want to be a good hitter, that's actually a pretty good start at the things you need to be doing. There's a reason that the all time leaders in GIDP are Yaz, followed by Rice, Evans, Papi and Teddy. HIDPs have a whole hell of a lot more to do with being a good hitter, than being a bad baserunner.
Yes if you have speed you can avoid double plays from time to time, but again, that has very VERY little to do with baserunning skill. Madly scrambling in the general direction of first base is a talent thing, not a skill thing. Meanwhile, double plays are a direct consequence of being a high quality contact hitter who stings the ball. The harder you hit it the more likely you'll HIDP because you're giving yourself less time to get to the base. Again, this is not a baserunning issue, especially not where it concerns Pedroia. His problems with double plays rarely have anything whatsoever to do with baserunning skill. They're the natural consequence of his very high ability to make contact with the baseball.