Mostly temperature, but volume has some effect.
My error, not Boyle's Law, I should have referenced the "Ideal Gas law", PV = nRT, where P is pressure, V is volume, n is the amount of gas (actual number of gas molecules), R is a constant and T is temperature. So as temperature drops in an enclosed space (V is constant = headspace) P must decrease... and vice-versa.
By keeping a bit of pressure in the fermenter (to add gas molecules as temperature drops), I am increasing 'n' as T drops to maintain a constant P with the gas of my choice, CO2 in this case. A balloon will do the same thing, but does it have enough 'n' to compensate for the temperature drop? Yes if the headspace is small enough. The ratio of headspace to beer is not completely relevant (the beer does contract very slightly, increasing V, but probably not enough to matter) but the volume of headspace determines how much gas is in there.
Bottom line: Cold crash to clarify beer. Some O2 might get sucked back in because of the temperature drop. One can force a little CO2 in there instead of allowing O2 from the atmosphere, there are several methods.