What does it take to get a hit with runners in scoring position? It takes courage to swing at a small white sphere thrown at an incredibly high velocity from a man whose job it is to manipulate the speed and movement of the baseball. When runners are in scoring position, there is no doubt that the pitcher is trying as hard as he can to make sure the batter does not hit the ball well. In the same respect, a hitter is also trying his absolute best to connect the bat with the ball and drive it to an open spot on the field. One can say that the pitcher and hitter are always trying their hardest, but everyone can agree that the stakes are much higher when there are men on base close to scoring a run. The reason why AVG is a better indicator than OBP when runners are in scoring position is that usually a walk will not produce a run, while a hit will produce a run. For instance with a runner on second, even a single will more often than not score the runner whereas a walk will not even move the runner to third. Now, sometimes a hitter does not have the choice- the pitcher will not pitch them strikes- but this is not reflected on his AVG. The AVG with runners in scoring position is an indicator of the likelihood the batter will produce runs with the swing of his bat.
However, if we decide that AVG with runners in scoring position is an important stat to keep, then there should be a stat kept on pitchers as well. If the same at bat is documented by statisticians equally between pitchers and hitters, then the two statistics will be more comparable and thereby tell a more accurate story of an important situation.
I'm not a huge fan of AVG being the ultimate stat that hitters are judged on, but it certainly does say something when a hitter can step up to the plate and produce in a high-pressure situation. If enough of these at bats are documented, then there will be enough data to interpret, and perhaps some valuable information can be inferred about the hitter from the data.