If the hand is part of the ball then the inverse is true and the ball is part of hand.

10-6-1: A player shall not shall not hold, push, charge, trip or impede the progress of an opponent by extending arms.......



The fact that he's holding the ball when this happens doesn't change anything.

Where's that rule found?

Off the top of my head isn't there something about a ball handler holding the ball and the defense makes contact with the hand, and this contact shouldn't be a foul?

It's been reworded recently, but here's the rule:
"It is legal use of the hands to reach to block or slap the ball controlled by a dribbler or a player throwing for goal or a player holding it and accidentally hitting the hand of the opponent when it is in contact with the ball." (4-24-2)

This wording has been changed, but it's really just a clarification. It does not, however, say the hand is part of the ball. That old adage may provide accurate understanding of the intention of the rule, but it falls apart when we attempt to apply it to other situations.

Let's Go To The Videotape ...
 

4-24-2: It is legal use of hands to reach to block or slap the ball controlled
by a dribbler or a player throwing for goal or a player holding it and accidentally
hitting the hand of the opponent when it is in contact with the ball.

From the list: It is legal use of hands to accidentally hit the hand of the opponent when it is in contact with the ball. This includes holding, dribbling, passing, or even during a shot attempt. Striking a ball handler, or a shooter, on that player's hand that is incidental to an attempt to play the ball is not a foul.

An Age Old Question ...
 

Let's keep it simple. Ball handler uses the ball to push a defensive player away, gaining an advantage. It's a foul. Is it a technical foul (noncontact live ball), or a personal foul (contact live ball)? This question had been around a lot longer than the Forum, and has been discussed on the Forum numerous times. It centers on the definition of contact: skin to uniform, uniform to uniform, ball to uniform? How about chair to player, à la professional wrestling? Let the rulebook language dissecting continue. Maybe we'll come up with a definitive answer this time? Are you paying attention Theresia Wynns?

https://sp.yimg.com/xj/th?id=OIP.M6b...=0&w=300&h=300

In the play I posted there was no advantage gained. Maybe a disadvantage for falling and throwing the ball to the other team, but that was his own fault.

A Riddle Wrapped Up In An Enigma ...
 

If the official deemed that there was no foul, then we can't discuss whether it's a technical foul (noncontact live ball), or a personal foul (contact live ball)? Too bad. I was hoping somebody would bring some new insight into this long standing debate.