Yes, but for very different reasons. Admitted patients were frequently at the point of difficulty breathing. When lying on your back, gravity makes your lung capacity smaller, when on your stomach, gravity makes it larger.
The increased survival was simply due to getting more air at a critical time.
When sleeping on your belly, doesn't your back "push" on your lungs? There's then more mass to compress your lungs than when sleeping on your back.
That would make sense. I wonder if, laying on the stomach is actually freeing the phrenic nerve, allowing the diaphragm to work better, and therefore providing more oxygen.