No, pitching is what happens before the ball reaches the plate. Defense is what happens after the ball reaches the plate. It's not difficult to understand.
To me, including defense in a pitching award is like when they give out gold gloves based on how good of a hitter they are (ie. Adam Jones). They are two different things with two different awards. Why even bother having a pitcher gold glove if they are the same thing?
The whole way they do awards is stupid, but it's difficult to understand why people can't agree on this simple concept. The Cy Young Award is for the best pitcher, the Hank Aaron award is for the best hitter, the Platinum Glove is for the best fielder, and the MVP is for the best overall player (a combination of pitching, hitting, and fielding). It's nice and tidy, one award for each aspect and a combined award. There is no need to combine pitching and fielding into one award.