Reddit mentions of Relief from Headache

It's possible that laying on his stomach created stress in his neck muscles since he was constantly tilting his head.

Disclaimer: I am related to the author. There is a book written by one of my relatives that might give a better explanation. The author is a neurologist and has conducted a number of studies on people with headaches, and has had a very high success rate with patients who actually do the recommended exercises. These exercises essentially stretch out the neck muscles, relieving tension and in most cases chronic headaches (including migraines). While I have never personally had to do the exercises because I don't get headaches often, I have talked to a number of the study participants and the response was very positive from those who did the exercises (many people stop after the first couple days). If I remember correctly the exercises are done about 6 times per day and take only a couple minutes a piece.