I have the same on my 07.
I don't think it's moisture inside the door cavity itself. Instead, I believe it's water caught in underneath the black wiping strip along the top edge of the door. There's space behind the strip, between it and the glass and wash water can collect there. As the dry glass goes down, this water is transferred to the window surface. (As subiesailor said, the so-called "seal" at the bottom of the window may still be wet.)
Also, the black wiping strip isn't all that tight against the window (to reduce load on the window motors), so as the wet window comes back up, the water isn't wiped off and held below as might a windshield wiper; instead, the water tends to be smudged around, showing up as streaks and drops.
I have the same on my 07, and also on my previous (not Subaru) car. I found that if I leave the windows up for a longer time after a wash, e.g. overnight (presuming in a dry environment), the problem didn't appear after the window was subsequently lowered. (Presumably, the water dried away.) But, if I lowered the window soon after washing the car, and left it down, the next day it would come up dry, but marked by water spots. The water causing those spots could only have been deposited on the glass on the way down. (If it were high humidity inside the door, I would thing it would tend to form a film, like dew, and not distinct water drop type stains.)
Another approach I tried was after washing, I used an air compressor nozzle to blow air between the that wiper strip and the glass. A lot of water came out. After that, I tried lowering and raising the window and the water streaking etc was mostly gone. But this wasn't something I wanted to do every time.
I also that a piece of blotter paper, or thin absorbent fabric, slipped down between the glass and the wiper strip after washing would soak up most if not all the trapped water, but I haven't tried this.
Just my take on something I've lived with for some 10 years now.