If that's the limited perception, then the cure is simple. Just stop doing it. But I'm sure everyone in this discussion appreciates that recovery is not so simple. Guilt, shame, fear, distorted perceptions, are all symptoms of the disorder as well. The internal life of the person with the eating disorder, needs to be respected and understood with compassion and intelligence.
Recovery covers a lot more territory than eating or non-eating behavior.
You also mentioned another big block to recovery from compulsive overeating is an overconcern about what others think vs. how the overeater thinks, feels and experiences the world. Briefly, I'll try. An aspect of the symptoms of an eating disorder is the desire to be perfect. Often the person struggles to maintain an image of perfection, even to the point of lying and using other forms of subterfuge to convey the perfect image. Also, people in the eating disordered person's life may come to expect an impossibly high standard to be maintained.