Seems to me that the only way that pivoting and twisting on the ball of the foot would turn you far enough to turn your head away from your opponent is if your stance was too narrow to begin with. Or, to put it another way, the stance is too sideways.
My coaches teach both ways, but they say this: that you should use the twist when throwing it as a lead when you are out boxing since your lead side hip isn't loaded. When throwing the lead hook off a combination (the hip is already loaded) the choice is yours as long as you don't overextend.
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