[just another ref]

Originally Posted by Jurassic Referee

case book play 4-12-6 referencing throw-ins says "The throw-in ends when A2 touches the ball, but the backcourt count does not start until A3 gains control. That means that neither player or team control has been established because either is needed to have a backcourt violation as per 9-8.

But this doesn't answer the original question. In this particular situation, the point is that the count doesn't start until team control is gained. The point is not how team control is gained. This is a situation that one might never see, but the series of batted passes would seem to constitute team control, whether an individual player ever caught the ball first or not.