You can think of your airway as tube of cartilage and soft muscle. As we age (there are also other contributing factors) this tube may be narrowed or collapse under the weight of adjacent tissue. Excess weight (more adjacent tissue), alcohol consumption (more tube muscle relaxation) also contribute to the narrowing/collapsing of this tube.
The airway tube has the least amount of pressure from adjacent tisue when you are on your side. And the highest amount of pressure when lying on your back.
What parent is dismissing is that Positional Sleep Apnea is a fraction of all sleep apnea cases. I.e. his solution of sleeping on the side would 100% resolve sleep apnea for a fraction of all sleep apnea patients but certainly not everyone.
Source: Did contract work for a sleep apnea startup.