Yeah...it happens. It's called aerophagia and while they comment about air swallowing implies the mouth being involved it doesn't necessarily mean mouth breathing.
wiki/index.php/Aerophagia
What happens is the air gets into the esophagus because the airway and the esophagus is combine until they split off with one part going to the lungs and the other part going to the stomach.
Air gets in the esophagus and there's a little sphincter at the esophagus and stomach junction. It's called the LES or Lower Esophageal Sphincter and sometimes that sphincter just doesn't keep the door closed well enough to keep that extra air from entering the stomach.
Maybe it's weak...maybe it's damaged from GERD...maybe there is a bit a a hiatal hernia. Whatever reason the air gets into the stomach and no where for it to go except with either burping or farting.
If it's real bad or really annoying or really painful or really makes a person ill...there are some things that can be done to limit that side effect that is unwanted.
If one big burp or big fart resolves the issue I wouldn't worry about it.
If it's really a problem the first thing to try is some pressure adjustments usually adding more exhale relief if possible and if not possible maybe some pressure changes. Sometimes just a little reduction in pressure will relieve the problem.
I may have to RISE but I refuse to SHINE.
