Cause the coaches don't know the #@$!* rules! And they write the rules. The main reason a team doesn't lose the arrow on a foul during a AP throw-in it is a huge advantage to the defensive team to foul during a AP throw-in to get the arrow switched.
Sounds like you handled the situation correctly by taking care of everything right away and not waiting until the next held ball to try and remember what happened previously then getting in more trouble. And you handled the coach as best as you could.
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