We researched the latter recently and found out, that this idea was spread after the war so that the children would not eat too much of the freshly baken bread, because it tasted better. No health implications at all.
My parents had limited vocabulary, but in a way they meant the same thing. Stale air (a hopefully faithful translation from my language) can have many meanings, but in context it means air with high CO2 concentration. I'm wondering how much of this is also the disconnect caused by fast technological progress and evolving language with it.
This leaves aside parental scorn/ignorance as you describe it. Sounds like stressed-out parents, if I may say so. However, I don't know how future generations will get better at it, only that you may get better at it.
Of course it varies greatly depending on the person, temperature, state of immune system, humidity, etc.
But it's just the opposite of hot tea helping you cough less.