I think this behavior comes from the webcam, and not Skype. I have actually seen this exact behavior with the Microsoft LifeCam, which often auto-changes the width of the video stream. The larger width will show "people on the sides," and the more narrow width does not.

I believe that the LifeCam looks for movement in the peripheral area. If there is no movement there, the LifeCam will truncate the sides of the image. I have sometimes been able to force the sides to appear by waving my arms off to the side.

When I first noticed this happening, I was surprised that many "people on the side" don't move or talk at all, thus triggering a truncation. But I started looking for this, and most "people on the side" barely move at all.

In my experience, Skype video quality tends to degrade by simply freezing the screen. I have also noticed this behavior when Skype was off entirely, when recording a video of myself. So I'm pretty sure it's the webcam itself auto-controlling the width, and not Skype.