You own link points out that the difference between humid and dry air in terms of heat capacity is a low single digit percent. Unless you can reduce the humidity from "a lot" to "basically nothing" and lose only a couple of degrees in the process (highly unlikely, completely impossible if your method consists of opening windows/doors in the winter) it is going to cost more energy to vent out the humidity and heat dry air than it is to just heat the humid air that's already near temp.

Just because a rental contract includes a clause doesn't make the intentions of that clause consistent with reality.

Furnaces dry out the air. Human activity can contribute moisture to the air. But the net effect is usually to leave the interior air dryer than the exterior air. Depending greatly on your lavatory ventilation.

Where I live, allowing outside air in greatly increases the inside humidity. And I would guess this is true for most people given the widespread complaints of dry winter skin and bloody noses. Which is the product of increased furnace operation.

> Venting significantly reduces the humidity of your air

Even when it's raining outside, etc?