This is never an argument I would use.
I would say training methodologies matter, styles not so much. If you train something properly, in an alive manner against fully resisting partners, then you will learn what works and what doesn't, and everything else falls by the way side unless it helps reinforce what works.
I would say it is impossible to acheive true Mushin without training properly. Also I don't think the idea of Mushin negates the idea that a style doesn't fight. How else are going to achieve Mushin if you never train a style properly to develop autonomous responses.
Mushin as an idea is universal, if you train properly you get to the point you just react. Even in Non Asian styles you still get to the level that you acheive Mushin you just might not call it as such.
However, what you have honed at that point will be what you do, and still be in the realm of what you have trained.
For example, throw a leg kick at a Thai fighter, notice he will check the leg kick in the manner he has practiced all his life, and he will not think about it. Throw a leg kick at a kickboxer, notice his immediate reaction is to absorb it while countering with a straight right.
Both are done without thought, they are empty minded responses that come from training for years. However, stylistically they are both completely different in how they approach or counter that particular technique. Is either one more right than the other?
Rickson Gracie is a big proponent of Mushin, though he calls it something different. However granted his approach to a fight whilst in Mushin is vastly different than Mas Oyama's approach with Mushin would have been.
Styles mean something absolutely, how you train is going to be the way you fight. But it doesn't mean one in particular better than others, more that it is a different approach. Provided you trained properly, and the quality of instruction you have is how effective you will be.
Keep in mind, Mushin doesn't mean you can't get your butt kicked, it doesn't mean you can't lose, get shot, get stabbed, or just get out punched. It just means you are reacting without thinking, your reactions and movements are automatic, not contrived or having to go through conscious thought.
The truth is in a real fight you are going to do what comes natural period, that is where good training vs. bad training comes into play. If you have trained properly, your techniques and reactions are effective. If you have trained improperly, you will know it exactly then, when you aren't doing any technique but turtling up, or wildly swinging. You are reacting naturally, and your training didn't make your techniques natural reactions.
I think most people who answer this way are all thinking in one sort of same vein... that "it is the fighter, not that style" and to a degree that is true. Some people have natural instincts, and physical attributes that may make them more effective in a fight, or even different insights and training.
But that is a small part of it. In the end training methods, and quality of instruction matter as far as effectiveness. Regardless as to how you deal with a punch (block, duck, slip, evade, crash, or trap) the fact that you stop that punch from hitting you is the bottom line. You won't be able to do any of those things without it being Mushin and done automatically. Stylistically your reaction is going to depend on your training. A boxer would slip, a Karateka would block, etc. Both are effective at the bottom line but both handle it in different ways.
Just my two cents.