In or out of bounds on save type play?

[hoopguy]

Saw this happen in my lunch time pick up game today and it made me wonder the ruling...

Ball is batted toward sideline near the division line. A1 is first to the ball and bats it forward. A1's momentum carries him out of bounds. A1 then steps in bounds and dribbles the ball. In pick up this was an automatic out of bounds violation. I believe this is actually the right call as well because of 9-3-1 'Note: The dribbler has commited a violation if he/she steps on or outside a boundary, even though he/she is not touching the ball while he/she is out of bounds'

The reason I am posting is because of case play 7.1.1 situation D. In this case play the player saves an errant pass and steps back in bounds and is allowed to dribble the ball.

I believe it could be argued that if the player in my example had his first touch push the ball ahead and then went out of bounds then that could be considered the save and he could be allowed to dribble based on the case play above.

In real life I would call the situation I witnessed an out of bounds violation but these two opposing rulings seem to have some overlap.