It means don't try and manipulate your breathing in order to try and save gas. Just breathe. In a stressful situation of course gaining control over the breath is good and necessary to prevent panic, etc, but that's not the context of the discussion.
I instead think that breathing control, as in Yoga, is a powerful way to control both your body and your mind. As already said, the goal is NOT to minimize SAC, but to breath more efficiently, avoiding CO2 accumulation and reducing the effort required. SAC reduction is a byproduct, it should never be the goal.
But if the diver does not practice proper exercises for learning how to
always keep control of his breathing, there are little chances that he suddenly will breath properly under stress. What instead I often saw is that inexperienced divers, under stress or heavy muscular load, or panic, tend to make their breathing even shorter, accumulating CO2, and loosing entirely control of their breathing.
SAC explodes, but CO2 accumulates as the short breathing is inefficient, and the apparent lack of air can cause a rapid, uncontrolled ascend, which instead should be always avoided.
For me, breathing control is a tool, for keeping control and remaining relaxed. And the goal, as I already repeated, is never to reduce SAC, but to ensure proper elimination of CO2 and avoiding the risk of going to dyspnea.
Yoga is good way to learn breathing control. Another one is following an advanced freediving course (Apnea Academy or the like). In both cases, the training exploits explicitly the relationship between breathing and brain control.