I think a large part of the reason for leaving both eyes open is so that there is no tension in the shooters face, or mind. It takes a conscious effort to close one eye. I watched the biathlon the other day, and most of the athletes used blinders. This is so that they can leave both eyes open but only see the sight picture. Thus keeping the face completely tension free.
My eyes are about equal as far as dominance, so they will switch back and forth. I can usually blink my left eye to get the picture back to my right eye. The smudge may do the same thing. I'll have to try it.
PS. Those biathletes are amazing. I have to take a break packing my rifle from the truck to the bench before shooting.