Stress and burnout affect different people in different ways: some people get depressed, others develop chronic pain (fibromyalgia, ME), others have chronic fatigue etc.
As for the psychological factors that seem to be important: motivation, goals and emotions all seem to play a large part.
While you're correct that CFS is not entirely psychological (functional would be a better term), it does appear to be mostly caused by psychological factors. If you look at the main triggers for CFS they are: job stress, relationship stress, and viral infection - and there is some doubt as to whether the viral infection is a cause or just a symptom of a weakened immune system.