oxygen in bottle head space

I have read in a couple of different places recently a statement that, when bottle conditioning, the yeast only consume the oxygen dissolved in the beer and don’t consume the oxygen in the head space. While that is true, it seems to me that it overlooks the fact that as the dissolved oxygen content drops the partial pressure of the oxygen in the head space will no longer be in equilibrium with the oxygen in the beer and oxygen will diffuse from the head space into the beer, where it will get consumed by the yeast, causing more to diffuse into the beer to maintain equilibrium between liquid and gas. It seems to me that this process will eventually stabilize with an equilibrium concentration of oxygen that is very low in both the beer and the head space. Is that wrong? If so, why?

Keep in mind that oxygen will continually seep into the bottle through the sealing compound in the crown cap.  Personally, I wouldn’t be too concerned about it though.