I believe that the term diffusion is often not understood. I'll try an explanation:
Diffusion is about a physical equalization of concentration differences between liquids and gases. Diffusion-permeable materials can be absolutely airtight. In practice, this means that in an enclosed space (where you cannot blow through, so it also passes the Blower-Door-Test), a concentration exchange can take place if the walls are diffusion-permeable (not to be confused with airtight). Materials can be diffusion-permeable for specific gases or liquids and not for others. From this understanding it becomes clear that a room with walls diffusion-permeable for CO2 can contribute to a concentration exchange without the air volume inside the house coming into contact with the outside air. During shock ventilation, the exchange rate is significantly dominated by the air exchange effect. It would be a mistake simply not to ventilate a house with diffusion-permeable walls. This is not a question of "either/or."
Regarding an air movement that comes from inhaling or exhaling through the mouth and nose, the comparison is of course off and the childish idea that walls "blow" is indeed ridiculous.
And AT THE SAME TIME:
A lung would not be functional without diffusion. Breathing involves a gas exchange between the alveoli and the blood. Here, one cannot—oh wonder—blow directly through the lung into the bloodstream (to put the Blower-Door-Test into this context).
Regarding the function of breathing in the form of oxygen transport into the bloodstream and CO2 transport to the exhaled air, the comparison is quite good, because it is about the equalization of concentration.
It can thus be stated that a diffusion-permeable construction is helpful for the concentration exchange of gases when this concentration equalization has a significant influence on the composition of the indoor air. This is measurably proven to be the case regarding CO2 and humidity.