Research "torque tuning"
Having the sight extended does not produce misses in azimuth. But the further the sight is extended, the more it is displaced in azimuth if you torque the bow. Sure, it makes no difference in the angle that you torque the bow -- but to put the sight pin on the target, you have to move the bow laterally more for an extended sight than you would for a sight that is not as far out. It is that lateral movement that results in the miss.
The premise of torque tuning is that there is a "matching" set of extension between how much the sight is extended and how far back (overdraw) such that the errors due to torque cancel each other out.
The basic concept is that if the sight pin and the arrow rest were both on the axis of rotation, torque would generate little to no miss. If just the rest were moved to overdraw, torque would cause a miss to one side. If just the sight were extended, torque would cause a miss to the opposite side.