Does the amount of water vapor air can "hold" depend on the temperature of the 'water' or the temperature of the 'air'? 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!
 A: 
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.

This isn't quite right.  If you were studying the liquid/vapor equilibrium in a small, closed container, this would be the right idea.  However, the atmosphere is somewhat more complicated.
The temperature of the water vapor is equal to the temperature of the air, not the liquid water. In a large, dynamic system like the atmosphere, the air and water are generally not in thermal equilibrium. As a result, the threshold (in terms of partial pressure) past which water vapor will condense into clouds or fog is a function of the air temperature, not the water temperature.
As an example - warm air is said to be able to hold more water vapor.  Technically speaking, this is because the water vapor which is mixed with warm air is itself warm.  If that warm air flows over cold water, the air (and the vapor mixed with it) cools down, decreasing the vapor pressure.  As a result, this now-cool air becomes supersaturated and condenses into the fog which so frequently surrounds large bodies of water.
As a second example, when warm, moist air rises, it cools via adiabatic expansion.  Since the air temperature drops, so does the vapor pressure of the water vapor it's mixed with, which leads to the formation of clouds.  This is why storm systems tend to form at cold fronts; the cool air sinks below the warm air in front of it, pushing the latter upward like a snow plow.

You're right that, from a certain point of view, the only relevant player in the game is H$_2$O.  The temperature of the liquid water determines the evaporation rate, while the temperature of the water vapor determines the vapor pressure and condensation rate.  In a large, complex system like the atmosphere, the temperature of the water vapor can be identified with the temperature of the air with which it's mixed, while being relatively decoupled from the temperature of any nearby bodies of liquid water.  In this sense, it is reasonable to talk about the capacity of the air to hold moisture.
