My reference to "inbounds or out of bounds" was based on 7-6-1, which states that the throw-in must touch another player inbounds or OOB before going OOB untouched (similarly in 9-2-2).  I had incorrectly assumed that the "or OOB" was also included in the definition of when the throw-in ends.  But it's not.
I'm sorry if I've confused people.  I'm a little confused myself now.  How could the throw-in NOT end if it is caught by a player who has one foot OOB? 

  It's not a throw-in violation, right?  B/c the thrower has not violated 9-2-2.  Hmmmmm.
So A1 has the ball OOB for an AP throw-in.  A1 throws the ball and A3 catches the ball with one foot OOB.  We 
have to switch the arrow here, right?  But if we say that the throw-in doesn't end when A3 catches it OOB, then we can't switch the arrow.  So why isn't that "or OOB" included in the definition of when the throw-in ends?
I must be missing something obvious.