I'm experimenting with the Franck Tchang Acoustic Resonators right now which are very potent in how they operate tho exactly how or why is hard to fathom. But never mind that. The point here is that the inventor's explanations started me thinking along certain lines that intersect with your question.
1/ The air in the room is in the signal path. Everything that's between the source and our ears (where sound is recognized *as* sound) is. Without the air molecules, the pressure waves generated by our speakers couldn't propagate. So the air is part of our system.
2/ Air is everywhere around us. Every air molecule is connected to every other one around the globe (except for rooms or containers that are literally airtight and sealed).
3/ When we close the doors to a room, it's not really a sealed container since there's leaks to the outside as is plain when you consider how much sound you can still hear outside the room.
4/ Especially in the lower corners behind the speakers but also the upper corners and then the corners behind the listening seat, there's zones of high pressure.
5/ If it's windy outside, there's high pressures exerting themselves also on what's inside the house (again, the only way to avoid that is to be hermetically sealed off.
In the "Franch View Of Things", unequal pressure distribution in a room causes negative acoustic effects and a lot of low-frequency pressure zones overdamp high frequencies to mask air, recorded ambience and micro detail. His devices -- don't ask me how -- "pierce" or "neutralize" these pressure zones as though, very basically speaking, someone drilled holes in the corners of your room to drain the pressure buildup outdoors. As you can imagine, that translates to sounding as though your room got wider. Plus, you can play louder without causing "room lock" and "overload". Bass gets better etc etc.
Once you start viewing the air in the room as an active element (it's elastic, it compresses) and realize that the air in the room connects with the air outside the room (unless yours is truly airtight), then it makes sense that pressure build-ups in this air will have an effect on the sonics. Altitude comes in as does humidity.
I don't mean to sound as though I really understood this stuff. I'm just starting to think along these lines to comprehend (attempt to comprehend) how these small resonators work. That they do is without doubt. And your question struck a nerve in that it looks at things from a similar angle, not necessarily having answers yet but at least starting to ask some interesting questions.

So it's really not an out-there question. For sound to propagate, we need the air as carrier as it were...