[Nevadaref]

Originally Posted by Nu1

As you described, A1 caught the ball, pivoted, and threw the ball down court.
If the ball hits the floor before A1 touches it, it's legal. If A1 does not allow the ball to touch the floor first, it is illegal.

However, would it be a travel or an illegal dribble? It seems the rules would indicate a thrown ball that is retrieved, that didn't hit the floor, would be (a) an illegal dribble, if the player's pivot foot was on the floor [when the ball was thrown], and (b) a travel, if the player's pivot foot was off the floor [when the ball was thrown].

[I added a phrase to your post for clarity.]

You are right. What most in this thread have been calling traveling is really an illegal dribble violation.

See the following case play:
4.15.4 SITUATION E: (a) A1 tosses the ball from one hand to the other while keeping his/her pivot foot in contact with the floor; or (b) A1 throws the ball over the head of B1 and then takes several steps before catching it. RULING: Legal in (a), but an illegal dribble violation in (b). In (b), since the ball did not touch the floor, the tossing and subsequent catch is an illegal dribble. (9-5)