I'm a 2nd Dan in Ki-do (korean, evolved from moo duk kwan and hap ki do.) My grand master, Grand Master Moon Ku Baek, had a saying: "If you want to be like superman, the secret is to breathe." Given that I've seen him and Grandmaster Kim break cast-iron wok covers with a chop I can well believe it. Their technique is much better than mine, but I can "concentration break" 2-3 bricks. A concentration break is a kneeling break, using meditative concentration to move the hand fast enough to break the bricks, without the benefit of the weight of the body as in a normal break. Without breathing, there will be no circulation and your arm muscles won't have the oxygen needed to move quickly. Knowing how to breathe can allow for "impossible" feats, simply because the tissues will be fully oxygenated.
As for body control, I can control heart rate +- about 10 bpm, and breathing rate down to about 0.5 breaths/minute, while still getting enough oxygen. Any high-ranked martial artist should be able to confirm this, breathing is critical. While the physiological mechanisms may not be perfectly understood it has noticeable and measurable external effects.