https://www.fiba.basketball/documentsI'm assuming the rule is the same as here:
Section 24.1.4
The following are
not dribbles:
• Successive shots for a goal.
•
Fumbling the ball at the start or at the end of a dribble.• Attempts to gain control of the ball by tapping it from the vicinity of other players.
• Tapping the ball from the control of another player.
• Deflecting a pass and gaining control of the ball.
• Tossing the ball from hand to hand and allowing it to come to rest in one or both
hands before touching the court, provided that no travelling violation is
committed.
• Throwing the ball against the backboard and regaining the control of the ball.
If fumbling the ball doesn't count as a dribble, then as long as you do not dribble again after retrieving the ball, there is no double dribble. Butler shot right away, didn't dribble again. I'm assuming NBA has the same interpretation as FIBA on this one.
EDIT:
Here's from the NBA rulebook:
Section II—Dribble
A dribble is movement of the ball,
caused by a player in control, who throws or taps the
ball to the floor.
a. The dribble ends when the dribbler:
(1)Touches the ball simultaneously with both hands
(2) Permits the ball to come to rest while he is in control of it(3)Tries for a field goal
(4)Throws a pass
(5)Touches the ball more than once while dribbling, before it touches the floor
(6)Loses control
(7) Allows the ball to become dead
(8) Otherwise gathers the ball. (See Rule 4—Section III-(b))
So from that section, the relevant parts would be "caused by a player in control" and "while he is in control of it". The bounce that happened after fumbling the ball was not a controlled action, it was accidental and therefore doesn't count as a dribble, hence you can't call a double dribble since no second dribble happened after fumbling the ball.