Question about being the first person to touch the ball after falling OOB

[Vyn]

My friend and I are having a debate about this. We were playing basketball one night, and this is what happened:

1) Player A shot the ball as he was falling out of bounds.
2) Player A falls out of bounds.
3) The ball hits the side of the backboard and bounces back toward Player A.
4) Player A stands up from out of bounds and sets two feet inbounds before being the first person to touch the ball for the rebound.

Did Player A commit a violation?

When you respond, can you please link us to the source of your information, because my friend doesn't believe anything unless it is in some rulebook somewhere, like from the NBA or NCAA or Olympics.

Thanks in advance.