You must be good if you can control your heartrate with your breathing
.
"parasympathetic response," which decreases your blood pressure, lowers perceived exertion levels during cycling, improves circulation, lowers your pulse rate,
yea...listen to Andrew Weil MD "Breathing", he discusses this braking effects of the parasympathetic nervous system on HR.
All this Biofeedback is used in freediving to optimize 02 demands/ consumption. I don't know anything about while cycling.
...but it's not bunk.