Runner on base out when hit?

[akalsey]

I took my sons to a AAA game today and saw R3 get hit with a fair ball in foul territory. The ball bounced on the line and hit him a foot or two outside the line. Ump called dead ball and sent him back to base.

The whole park was screaming that he was out because he was hit. My 8 year old asked me why he was safe (he'd been hit with a batted ball in Little League this season). When I explained why, he said "oh, that's why they run from third base in foul territory then."