I've a feeling this study is flawed. For a long time eggs were very bad because cholesterol. But for the past decade and a half we have learned that for most people eating cholesterol is not, itself, bad. Eating lots of saturated fat and perhaps lots of simple carbohydrates are more likely candidates for bad health. For eggs in particular, the long run studies say that ~1 egg per day is not bad, except maybe if you are diabetic.
Now I realize that the studies are different, and I don't have full article access so I don't know how they controlled for things like butter, but eggs in general are protein/vitamin rich and the protein and fat helps to feel sated at lower levels of calories than carbs and far more doctors and nutritionists are high on eggs than down on them. I think I'll eat eggs.