I dont claim to be a rules historian, but I'll explain it the same way it was explained to me 20 years ago by the former SAL league umpire who trained me.
It is the responsibility of the runner to avoid being contacted with a batted ball. For being contacted by a batted ball the runner is called out.
It is not the fault of the batter that the runner has been been called out. The batter has been deprived of his opportunity to realize the effect of his batted ball (either safely hit/or out). The ball is dead and the batter is credited with a hit. For scoring clarity purposes the putout goes to the nearest fielder.
Now I don't pretend this to be the exact answer, but it made sense to me back then. For rules on this, both OBR and NFHS agree.
For citation: NFHS rule 8-4-art 2 sect K
A runner is out when:
Is contacted with a fair batted ball before it touches an infielder, except the pitcher,and the umpire is convinced that another infielder has a play.
For scoring:
NFHS Rule 9-4-art 2 c
For runner being called out because of beng hit by a batted ball, the putout is credited to the fielder who is nearest the ball at the time.