And the increase in oxygen intake, (as minimal as it is, being more down to surface area of alveoli than amount of air inhaled), is not what lowers the heart rate in stressed environments.
You think this kind of breathing was invented by these guys? Its a technique used by people as diverse as yogi's and opera singers. Certainly over time, the lungs can be conditioned to recieve and utilise more oxygen, but even with such people conditioned to do so, in a fight or flight situation, it is not the oxygen levels aquired from deep breathing that lower the pulse rate, it is the triggers sent tot he autonomic nervous system to shut down its emergency physiological processes.
Also, at this point, can I ask you if this is a subject so dear to your heart that you feel it right to take a tone with me? Is this the pi$$ing contest you desire?
The reason I said i dont need to read those books is because I have a whole stack of literature on the respiratory system that I had to learn as part of my academic studies in sports science. If this came off as dissmissive, then sorry, its just I already have a solid grasp of how and why the body works the way it does.
At the end of the day, deep breathing exercises can lower pulse rate. On that we agree. You believe it is down to oxygen content in the blood, I disagree, as I know the effect it has on other aspects of the physiology. If thats an impasse you want to butt heads over, then you have less planned for your weekend than I do