I think we are missing something.
The question needs be asked. Where does the fresh air enter the cabin?
If you have relatively low pressure just outside the rear outflow valve (remember there is a valve at the front as well, plus an exhaust port), the air will flow
out through the valve not
in through the valve. This flow will
cease when the pressure differential equalizes (that is, the local pressure on either side of the rear outflow valve.)
For the pressure not to equalize, and therefore allowing the flow of air to continue from high pressure (inside the cabin) to low pressure (outside the cabin) through the outflow valve, there must be air flowing into the cabin to replace the outgoing air.
Just like sucking the end of a bottle. The pressure differential is there (between the inside of the bottle and the ambient atmosphere), but because there is no incoming air to replace the small amount of air that has been sucked out, the pressure inside the bottle and the pressure just outside the bottle opening equalizes (the lower pressure inside your mouth), and the airflow stops.
Put another hole in the bottle (preferably at the other end) and the air starts flowing through it.
The aircraft needs that other hole too.
Could it be the forward outflow valve? Afterall it automatically opens when airbourne with low differential pressure. Perhaps there is an airflow reversal through that valve.
[Edited with some extra brackets added to make it clearer.]
