Runner Hit by Ball

[brandda]

Had a situation the other night in a Majors game with man on third, two outs and the batter hit a line shot down the third base line which hit the runner who had not yet moved off of the bag. I judged the ball fair and that it had not passed an infielder so the runner was out. The coach erupted saying that he was not out because he was still on base.

I cannot find anything in the rules that talks about a base only that if the runner is hit in fair territory before it passes an infielder, he is out. Any thoughts?