[Back In The Saddle]

Okay, let me see if I understand this correctly.

If, as in the OP, the ball handler A1 has used his/her dribble...

If A1 fumbles the ball, he/she may take any number of steps and legally recover the ball (NFHS 4-21, 4.15.4D (d), NCAA 4-31.2). But unless the fumble touches another player before A1 recovers it, A1 may not dribble again legally. (NFHS 9-5-3, NCAA 9-7.1c)

If A1 attempts a bounce pass, which for whatever reason no teammate is there to receive, and A1 is the first to touch the ball after it has touched the floor, A1 has committed an illegal dribble/double dribble. (NFHS 9-5, NCAA 9-7.1, NCAA AR 88)

If A1 attempts a non-bounce pass, which for whatever reason no teammate is there to receive, and A1 moves beyond the prescribed pivot foot limits and catches the ball before it touches the ground, A1 has traveled. (NFHS 4-44, 4.44.3D (d), NCAA 4-70)

However, if A1 has not used his/her dribble...

If A1 fumbles the ball, he/she may recover the ball and legally begin a dribble. (The fumble-dribble-fumble maxim often quoted here)

If A1 attempts a bounce pass, which for whatever reason no teammate is there to receive, and A1 is the first to touch the ball after it has touched the floor, A1 has begun a dribble and may legally continue that dribble. If A1 recovers the ball in a way that ends the dribble, A1 may not legally dribble again.

If A1 attempts a non-bounce pass, which for whatever reason no teammate is there to receive, and A1 moves beyond the prescribed pivot foot limits and catches the ball before it touches the ground, A1 has still traveled. Having dribbled, or not dribbled, prior to this action is irrelevant.

Are any of those statements incorrect?