They do all the time. I saw a video where American police were yelling confusing instructions at a drunk guy clearly trying to do what they ask but unable to work out what they want and when he fell over they opened fire at him because he made a quick movement.
But its almost justified. I have seen videos where someone moves their arm just a bit and the police start shooting instantly before I even know what has happened and a gun falls out of the dead targets pocket.
Thats just what happens when any random stranger could be carrying a gun. Its almost unheard of for someone to be wrongly shot by police in Australia (Probably has happened but its no where near like America)