who is out on fair ball hit that hits a baserunner

Question
Dr. Mark,
Runner on 3rd, 1 out, batter hits line drive toward third base and hits runner after he has left third base while he (and the ball) were in fair territory, ball picked up by 3rd baseman and he tags runner and throws the ball to first base. Umpire initially calls baserunner on 3rd out by the hit ball and then calls batter out as he did not beat the ball to first base.     After further consultation the runner on 3rd was called out and the batter was allowed to bat again.   Discussion then followed that the batted ball could not have been fielded by the 3rd baseman therefore the baserunner was not out by the ball hitting him, but by the 3rd baseman tagging him and the batter was then out because the throw beat the batter to first base.  More discussion followed that the runner on 3rd should have been called out when the ball hit him and the batter should have been allowed 1st base.

Answer
Hi Moe,

If R1 was hit by a fair batted ball off base before it passed an infielder (exc F1) the ball is dead, the runner is out and the b-r is awarded 1st base.

Whatever happened or didn't happen after R1 was struck doesn't matter as the ball is dead.

mark