I have a pretty different understanding of this topic, or at least a different way of imagining it. I figured I would post in case anyone else was still confused.
It's important to remember the difference between intrapleural pressure and alveolar pressure. The alveoli are open to the environment so alveolar pressure (i.e. the pressure inside the lungs) is really the same as atmospheric pressure. Intrapleural pressure is the pressure of the air in the pleural cavity in which the lung sits (the space between the lung tissue and the chest wall).
It's also important to note that no pressures are actually negative. Pressure can't be negative. But we refer to intrapleural pressure as "negative," which just means that it is less than alveolar pressure.
So, the intrapleural pressure around the apical alveoli is less ("more negative") than the intrapleural pressure around basal alveoli. Why? From what I understand, the answer is gravity. Gravity pulls the air molecules in the intrapleural space down from the apical area toward the basal area, making them settle in the basal area. The effect is:
-a higher ("less negative") basal intrapleural pressure. This higher pressure exerts a larger force on the alveoli, causing basal alveoli to close.
and
-a lower ("more negative") apical intrapleural pressure. This lower pressure exerts less force on the apical alveoli, causing them to be more open.
This is important because the differences in intrapleural pressure leads to differences in perfusion and that, in combination with differences in regional blood flow, leads to v/q mismatch in the lungs (physiologic dead space in the apices, shunt in the bases).
I think that answers OP's main question. If anyone has any other questions or if anything I've said is incorrect, feel free to let me know..