I'm not sure the others who have chimed in have succinctly identified the part of this "experiment" that makes it break down. So I'll put it this way:
You can't "take the same shot" in this scenario if you "mask off the edges." In order to get the same shot, you'll have to then step back from your subject. Stepping back from the subject increases the distance over which the camera has to be steady and therefore increases camera shake.
This is another good way to look at it.
Whatever way it makes the most sense to you, the fact remains that you have to consider the effective focal length, not the actual focal length, when calculating 1/focal length shutter speeds.