The amount of water vapor that the air in a large region (say a suburb) can hold should be dependent on the average temperature of the liquid water within that region. Not the air temperature of that region. This is because the evaporation rate of water is dependent on the water temperature (not the air temperature) since the water molecules obey a distribution similar to the Maxwell Boltzmann distribution. So if the water temperature rises, the evaporation rate rises and vice versa.
On the other hand, the condensation rate of water in a given region will primarily depend on the partial pressure of the water vapor in the air of that region. So as more water vapor fills the air, the condensation rate increases until we reach an equilibrium point when the evaporation rate equals the condensation rate. At this point, the air is said to be saturated and colloquially we can say that it cannot 'hold any more water vapor'. If we now increase the water temperature in the region, the evaporation rate will briefly exceed the condensation rate, filling the air with more vapor until a new equilibrium is reached. Crucially, this all depends on the water temperature and not the air temperature. At least according to my understanding (which may well be totally incorrect).
Yet I constantly find reliable sources that state in essence that the amount of water vapor air can hold is dependent on the temperature of the air and not the water. For example, "Dropping the temperature of moist air reduces its moisture capacity" (Cengel and boyles, Thermodynamics internation edition). Similarly, wikipedia states "colder air can hold less vapour, so chilling some air can cause the water vapour to condense". The only resolution I have at this point, is to surmise that these statements are actually wrong on a purely technical level but that they almost always provide the correct answer because of the fact that the water temperature in a region is strongly correlated with the air temperature of a region. Hence stating that "a rise in air temperature implies a rise in airs capacity to hold water" is almost always correct because a rise in air temperature almost always implies a rise in water temperature. Am I correct in my understanding? Is it true that reliable texts frequently get this issue wrong or is it my understanding that's faulty?
Any help on this issue would be greatly appreciated!