I want to make sure I get this correct. If there are 0.3 of a second or less it has to be a tap, and it also has to be the refereees decision if it was a legal tap or not. We had a game around here end like that last night. There was
0.1 showing on the clock with team A ahead by two and team B inbounded the ball and scored and it was waved off. I wasn't there but I heard all hell broke loose with coach, and fans and the refs barely got out.

That is correct. With .3 or fewer seconds on the clock at a dead ball, A shooter can not catch the ball and score. The only way to score is by a tap. We had very veteran officals blow this call during the semifinals of last years state tournament at the 6A (highest) level.

You are correct, with .3 left it has to be a tap. Of course if it goes and gets waved off the coach is going to go off. It depends on what happened. If the officials thought the player caught the ball and then shot, they are correct in waving it off. Also, if waving it off prevents you from going to overtime, the officials were correct in waving it off (kidding about that one of course).

Yes.
You understand it correctly.

Unless the tap was unusual, I can't imagine waiving off the tap with .1 left on the clock. If the horn went off prior to completion of the tap, it's more likely a timer error.

I guess they thought it wasn't a legitimate tap is the reason they waived it off. I guess no matter what was called in that situation someone is gonna be upset. Thank God it wasn't me this time.