[SAump]

But I would not be splitting hairs if I do point out that those words do matter if one were to look up the exact definition of a fair or foul batted ball.

The correct ruling regards a batted ball redirecting from the ground into the B/R or B/R's bat. It is ruled a foul ball just prior to hitting the B/R outside of the batter's box in these situations. This is the case of the swinging shot directly into the B/R's lower left leg while over fair territory.

The B/R is ruled out much more often for running into a fair "bunted" ball bounding in front of the plate. The batter's box is not a refuge and He does not have the right to a direct path to the nearest base through the bounding baseball. The runner must avoid contact with the batted ball. The same ruling would apply to any runner contacting a baseball while over fair territory.