Sharing what I learn here...

[bsnalex]

Ahem...allow me to throw my ISF ruleset in (that's what I always use because that's what British Softball uses...)

8.2.g.2 Batter-Runner is out when he interferes with a fielder attempting to field a batted ball.

It makes no distinction between a fair or fould batted ball. One could argue that a foul ball that appears to be rolling fair will have a F3 running hard at it to keep it foul because they know they won't have a play at first if it's fair, so the interference remains on the foul ball.

Incidentally, the ruleset also mentions that the runner may run beyond 3ft from the baseline to avoid causing interference.