[BillyMac]

You are correct. It's an illegal (double) dribble.

Throwing the ball against an opponent's backboard is considered to be a dribble.

And yes, if one officiates long enough one will see this happen, I just had one in a middle school girls game this past week.

This can get even more exciting if an opponent fouls the "thrower".

4-15-1: A dribble is ball movement caused by a player in control who
bats (intentionally strikes the ball with the hand(s)) or pushes the ball to the
floor once or several times. It is not a part of a dribble when the ball
touches a player’s own backboard.

Basketball Rules Fundamentals
19. A ball which touches the front face or edges of the backboard is treated
the same as touching the floor inbounds, except that when the ball touches
the thrower’s backboard, it does not constitute a part of a dribble.

4.15.1 SITUATION C: A1 attempts a pass to A2 during pressing action in A’s backcourt. The ball hits B’s backboard and deflects directly back to A1 who catches the ball and: (a) passes the ball to A2; or (b) starts a dribble. RULING: The pass against B’s backboard was the start of a dribble which ended when A1 caught the ball. In (a), the pass is legal action. In (b), it is a violation for a second dribble. (4-4-5; 9-5)

4.15.4 SITUATION C: After dribbling and coming to a stop, A1 throws the ball: (a) against the opponent’s backboard and catches the rebound; (b) against an official, immediately recovers the ball and dribbles again; or (c) against his/her own backboard in an attempt to score (try), catches the rebound and dribbles again. RULING: A1 has violated in both (a) and (b). Throwing the ball against the opponent’s backboard or an
official constitutes another dribble, provided A1 is first to touch the ball after it strikes the official or the board. In (c), the action is legal. Once the ball is released on the try, there is no player or team control, therefore, A1 can recover the rebound and begin a dribble.

9.5 SITUATION: A1 dribbles and comes to a stop after which he/she throws the ball against: (a) his/her own backboard; (b) the opponent’s backboard; or (c) an official and catches the ball after each. RULING: Legal in (a); a team’s own backboard is considered part of that team’s “equipment” and may be used. In (b) and (c), A1 has violated; throwing the ball against an opponent’s backboard or an official constitutes another dribble, provided A1 is first to touch the ball after it strikes the official or the board. (4-4-5; 4-15-1, 2; Fundamental 19)