You're right that binocular depth perception is just one of many cues, but your experiment will be tainted by cached binocular information. Recall that you can only actually see with any detail a tiny area represented by your fovea - the full image that you perceive is made up by moving your eyes over a scene and is of course aided by memories of what you expect certain elements to look like.
Here's another experiment:
Go to the same window but start out with one eye closed. Take note of what you see and try to judge how far away things are. After a minute, open the other eye and blink a couple of times.
Note the difference.