There is no question that H intended Burr to believe he was going to fire at him. Nor is there any doubt that H’s shot was so wide of the mark that he, an excellent shot, did not shoot at Burr.
Tell ya what. Go stand in front of a cop, pull out a gun, and fire it "wide of the mark" in his general direction. Hell, fire it straight up in the air. And you can even write a note announcing your intent to fire it off mark and leave it in a little envelope on your pillow for somebody else to find after you do it.
Assuming you survive the inevitable barrage of bullets your action provoked, there is not one courtroom in America that would find the cop unjustified in returning fire at you out of the legitimate belief that you threatened him first, making his action a matter of self defense.
Two grand juries indicted Burr for the murder of Hamilton.