http://www.youtube.com/watch?v=RxT7sprhEx8That is the play in question.
The four criteria for a backcourt violation (NCAA and NFHS):
1. Team control (and initial player control when coming from a throw-in)
2. Ball achieves a front court status
3. Team in control is last to touch the ball before the ball achieves a backcourt status
4. Team in control is the first to touch the ball after the ball achieves a backcourt status.
A team is considered in control of the ball when holding or dribbling a live ball inbounds or the ball is at the disposal of the throw-in/free throw team. A player is in control of the ball when they are holding or dribbling a live ball inbounds.
Now that we got that out of the way, the player in question bats the ball down twice...and it's close but the third bat could easily be judged as the beginning of the dribble....since it's the beginning of a dribble, by rule player control has been established. Thus it would be a backcourt violation.