If I remember correctly, as its been a while, breathing rate is controlled by the amount of CO2 in the blood. The brain stem (medulla oblongata) detects the lowered pH (due to carbonic acid, which comes from the increased CO2 concentration) and signals the diaphragm to breathe it out more forcefully. That could somewhat explain your source’s basis.
But then you’ve got the flip side of that - yawning. Again, it’s been a while since my undergrad A&P classes; yawning is caused by a buildup in carbonic acid too. When we get tired (sleepy, not exertion) our breathing slows down. It slows down a little too much and too soon. Our body responds by yawning - the relatively slow deep breath in followed by the deep exhale. If breathing was solely about the brain telling the diaphragm to get the CO2 out, we probably wouldn’t do the long breath in, right? Next time you yawn, pay attention to the breath in. It shouldn’t take too long for that opportunity, as yawning is contagious in a sense, and someone just mentioning it gets people yawning. I’ll bet you probably yawned a few times just my mentioning it here (and my boring you with this post). Also, scientists have observed the yawning being “contagious” in a ton of different animal groups.
Another interesting tidbit - yawning is common during relatively long breaks in physical activity. Like when a coach takes too long explaining something in between drills. It’s not because he/she is boring the team; I’ve had a few coaches say “am I boring you guys?” It’s because the breathing pattern is out of synch with the demands of the body and is catching up.
Another stupid thing I was thinking just last night: my daughter was doing yoga with her basketball team. Sitting there watching and hearing the yoga instructor telling them to breathe in and out, why did that mess with my breathing? Why is it our breathing pattern gets messed up when we hear people talking about breathing? Or even when we just think about our breathing? How many times did your pattern get changed a bit by my rambling?
It’s all pretty messed up thing if you really think about it. Something as simple as breathing.