Hes right.. It can actually be a sign of good heart health... Have you had an ECHO done? in my opinion, everyone should have one, just cause :) its a good thing to have.
I am not sure is this is what you are addressing, but Respiratory Sinus Arrhythmia, perhaps abbreviated (likely abbreviated) by the Doctors as Sinus Arrhythmia, is the natural increase in the heart rate as you breathe in and decrease in the heart rate as you breathe out.
This is a natural condition expected to occur in healthy individuals. Here (in part) is a more technical commentary on RSA (respiratory sinus arrhythmia) from an online site:
"Respiratory sinus arrhythmia (RSA) is heart rate variability in synchrony with respiration, by which the R-R interval on an ECG is shortened during inspiration and prolonged during expiration. Although RSA has been used as an index of cardiac vagal function, it is also a physiologic phenomenon reflecting respiratory-circulatory interactions universally observed among vertebrates. Previous studies have shown that the efficiency of pulmonary gas exchange is improved by RSA, suggesting that RSA may play an active physiologic role."
Hope this helps.