I find this thread to be very interesting.
I learned in school studying different braking systems that the increased surface area of larger brakes did in fact change the speed in which the rotors hit zero. Which should logically reduce stopping distances. But if what the op suggests is true then I appear to be very mistaken. I suppose it makes sense as you can lock up any wheel with any brake system with a simple press of the pedal. However, I cant help but wonder if there is some high end speed (say like 200mph) where the single pot caliper would fall off and not stop the disk. All logic would say that at some speed the friction of the brake pads will not stop the rotors.
I will say that for daily driving I would agree the size makes no difference.
And I looked up some statistics for stopping distances. and as the op said I found the sti did have slightly shorter stopping distances. And if the op is correct it is due to the tires. So if anything, a 2.5i with the sti tires will stop the same. I'd really like to see that tested.