[AtlUmpSteve]

I'm going to weigh in with Bret on this one.

The old rule said that a ball that was over the batter's head could not be a foul tip; it also said that a ball not over over the batter's head that went sharply and directly into the catcher's body or equipment was a foul ball even if caught by another fielder.

Nothing ever said what you (Deputy) are taking to be the inverse, that a batted ball not higher than the batter's head that was not hit sharply and directly to the catcher's glove could not be caught for an out. You are interpreting a ruling that does not exist because it seems to be the inverse; but it is not.

The inverse of a foul tip is NOT a foul ball; it is a batted ball caught for an out. All ASA definitions of foul balls (both past and current) refer to balls not caught, except the one hitting the catcher's body or equipment first.

So if this is not, by definition, a foul tip, and it is not by definition, a foul ball, it is the only remaining possibility; a caught batted ball is a live ball out, with runners required to tag up. Nothing about the batted ball that doesn't get higher than the batter's head, and is caught, makes it a foul (thus dead) ball.

In other threads, I have used the phrase that touching a bat never makes a ball foul dead. Only one of the definition of a foul ball makes it foul and dead. It appears you are confusing the location of the ball when caught (over foul territory) with the result of the catch; and that makes no difference to anyone but NCAA statisticians.