A tilt back headstock shouldn't need a string tree. My guess is he used it as a mute especially for the open strings. If his background was on upright he probably used open strings more as a transition for position shifts. So the sock might have helped keep the open strings as thumpy as the fretted ones. On the other hand, you'd think it would be easy to palm mute when using your thumb. Go figure, it was 58 years ago.