I was keeping the clock for a boys varsity tournament semi-final game. With about a minute left in the first half A1 steals the ball and gets a breakaway. At about the foul line he tosses the ball off the backboard and catches it for a slam dunk. The crew made no call. To clarify this, the player did not pick the ball up and toss it off the backboard, it was a one handed continuous motion off the dribble toss. He caught the ball and dunked it in the air. At the half Coach B asked about it and said he thought it was a travel. The crew said they were pretty sure they were right but would check it out and get back with him. Either way they made it clear the play stood and that they could not change it. At halftime we looked it up and the best we can come up with for this being legal is Article Rule 4, Section 4, Article 5 which says "A ball which touches the front faces or edges of the backboard is treated the same as touching the floor inbounds,...".

We think it was not a travel. Is that right?

The crew got it right! Legal

If the player didn't travel when he ended his dribble by throwing the ball off the backboard, then it's a legal play. Treat the ball being thrown off the backboard as a try. You can legally miss a try and then go get the ball.

I've got hot dogging, but no travel from what you described.