Batter in the batter's box

[SC Ump]

Of all places, there was a discussion over on the baseball boards about ASA and the batter's box. I started trying to reseach the FED softball rules and could not find this documented. I think I know the answer, but I want to make sure.

When a batter is taking his or her place to bat, my understanding is that their feet must be within the lines of the batter's box. To me, this has always meant that if a foot is on the line, but not at all touching outside the lines, they are legal. What's everyone else's understanding?

I would also like the rule reference if you have it, especially for NFHS.