My theory on instinctive shooting (yup, I'm one of those guys, too) is a little different than most, since although I believe the instinctive shooter is "aware" of the arrow he/she doesn't need to actually "look" at it. What they "see", in their mind, is a relation between the spot to hit and the imaginary line of the shaft created during the draw. The arrow point (a two-dimensional "sight pin") is not used and is basically irrelevant. The line of the shaft (a three-dimensional "flight path") is created by the mind during the draw as the shooter subconciously sees/feels the shaft (and draw elbow) 'lining up' relative to the spot. The "aim" is set subconciously by the mind visualizing (not by the eye looking directly at) the arrow as the draw is completed and alignment with the spot is deemed (subconciously) to be correct. The shot then happens.
I.e., the shooter does not need or even want to look at the arrow, at all, but he/she is aware of where it is in space relative to the spot. I think it's more like shooting a basketball than throwing a baseball. See and focus on the spot on the rim, execute learned shooting form subconciously, subconciously feel the arc needed based on subconcious calculation of distance (all the while visually locked on the rim spot and line...no fair looking at your arms or hands!), feel the ball launch from your hands towards the mark, follow through...and wait for the swish.
Your subconcious trusts that all this learned work will make the ball go where you are looking. With practice and lots of repetition, it actually does (amazing!!!...not really). Shots get harder as you move away from the basket (or target)...spots become smaller, there's less margin for error, more variables to affect the outcome.
It's a simple, subconcious calculation of what to do to hit something based on form and feel. You do pretty much the same thing when walking, eating, breathing, etc. "Instinctive"...done without concious calculation of the components of effort needed to reach the desired conclusion.
Or something like that.....
:D