Some misinformation or perhaps more correctly a lack of understanding eye dominance and related issues in shooters. Ideally a shooter should shoot 2 eyes open if they are physically able to do so. However there are eye conditions where focus (myopia or emmetropia) perhaps different for each eye may cause issues. Eye dominance, lack of dominance or shifting of dominance can very much affect the ability to shoot with 2 eyes open for many people also. Fatigue, age, eye strain, injury etc, etc can create issues. No one is the same and to try to give one blanket answer is incorrect and that mostly stems from ignorance of the issue itself.
I will also note that about 3-5% of the population is what is called "ambiocular" and I happen to be in that category. This basically means that there is clearly no dominant eye or that dominance can quickly shift between both eyes. What does this mean? There are some great advantages to being ambiocular but for shooting with 2 eyes open it isn't so great. Often the eyes will fight with one another so much the 2 superimposed objects can quickly shift and I mean almost instantaneously back and forth. It is also very difficult as an example to get say a front sight focus with 2 eyes open. Both eyes battling for dominance can shift focus instantly causing issues. Now the latter front sight focus part may not be an issue in combat style shooting but when your muzzle superimposed over your target keeps shifting it can wreak havoc. On the plus side, shooting from either side for accuracy is simple as there really is no true dominant eye, so if you close one eye it doesn't matter. Again this does not just go for ambiocular people, but for many people with varying eye or physical conditions. Age, injury and a host of other things can shift dominance throughout a shooting session. Having a solution to the problem is what is needed and not a suck it up and do it mentality. It is not a mental function but rather a physical one.
So what is the option? To either squint or close one eye to maintain dominance focus in the eye of your choice. At the moment we acquire sight picture is very very brief. The subconscious mind and the speed at which the eye reacts is blistering fast. So fast that for those microseconds in time where focus occurs means very very little in the realm of situational awareness. It is the same moments in time that a 2 eye open shooter will have their entire attention on the immediate threat. No difference. Many great combat style or competition shooters do just this. Now we aren't running around with one eye shut or squinting all the time, but one may squint only enough to be able to "see what they need to see" in order to get the desired hits. Being closed minded on the topic of eye dominance its related issues and how they might apply to different people does little to no good in solving issues related to physical inabilities rather than addressing a skill related issue. Having a solution for a shooter is key, not to just tell them too bad do it. The problem being is that people who do not have such eye or physical related issues that may create such conditions generally have no clue what others may or may not be seeing.
As an example I will squint one eye at the time of sight picture / sight alignment, whatever type of alignment I use, whether it is flash front sight, slide indexing whatever. However when I do a target transition as an example I am 2 eyes wide open for that split second or however long it takes, then when I am focused on the threat, my eye will slightly squint. How much depends on the type of focus that I need. It is not something that I need to think about it happens more quickly than my brain can make my fingers or body move.
In these video's I am not shooting two eyes completely open as I pull trigger. I only squint for a millisecond as I confirm alignment, during the draw, presentation, transition, reload etc, it is two eyes wide open. These are only to show how briefly you can squint or close an eye and not lose awareness.
http://www.youtube.com/watch?v=blFXUH-SIk8#t=2m5s
http://www.youtube.com/watch?v=pac1BcRc8dg#t=5m45s