When is the B-R "out of the batter's box"?

[umpman1]

Searching the Forum shows that this subject hasn't been addressed in the last couple of years and newcomers like me could benefit from the discussion.

The books (ASA, NFHS) are clear on what is meant by in the box
1) before the pitch is thrown
2) when the batter makes contact with the ball the first time

What is not clear is the meaning of the words used to define a foul ball (ASA Rule 1):
"Touches the batter... while the batter is WITHIN THE BATTER"S BOX."

A batter is out of the box during initial contact if one or both are on the ground, completely outside of the lines of the box. A pitcher is out of the circle if she has one or both feet on the ground completely outside the line of the circle. The fielder is out of play if she has one or both feet on the ground completely outside the out of play line.

It seems to me that WITHIN means that no part of the body is touching the ground outside of the line, but yet I know from reading old threads that this is not a view held by everyone on this board.

I am looking for a rational, substantiated ruling that I can teach my younger umpires. What is your interpretation?