Roughly. The issue is water trying to get out down the same tube air is trying to go in through. If you open the tap at the base, the water will eventually all get out. So the air pressure in the room prevents it draining. If you open the tap at the base, and then take the cap off the reservoir, water will come out a lot faster as air can get in easily.
The water physically above the reservoir will tend to push water out through the top cap. Moving the reservoir physically to the top of the case would solve that, but is inconvenient. Running a tube from the top cap out the top of the case is easy. There is then no water physically above the air inlet hole, so no pressure pushing water out through said hole.
The water physically above the reservoir will tend to push water out through the top cap. Moving the reservoir physically to the top of the case would solve that, but is inconvenient. Running a tube from the top cap out the top of the case is easy. There is then no water physically above the air inlet hole, so no pressure pushing water out through said hole.