Look at a state diagram for water. Below the critical temperature/pressure, increasing pressure drives the liquid/vapor equilibrium point toward more liquid/less vapor which enhances condensation in a closed container. Point for Doug.
Decreasing temperature does the same. Below the critical temperature/pressure the reverse is also true; increasing temperature enhances evaporation in a closed container. Point for Kevin/Mortimer.
Critical temperature is the temperature above which water cannot exist in a liquid state no matter how much pressure is applied. For water, that is about 374C or 705F. Critical pressure is essentially the vapor pressure at critical temperature; about 217.7 atmospheres or 3200 psi.
Also note that the pressures involved are the partial pressures of the individual gases, not the total pressure of a mixture of gases. In a container of atmospheric air at total pressure of 10 atmospheres, the partial pressure of the water vapor will vary depending on the absolute humidity of the air, but it will be much less than 10 atm.
The equilibrium point (mass of liquid vs mass of vapor) in a closed container is a function of both temperature and pressure. Doug, Kevin, and Mortimer are simply arguing opposite sides of the same coin.