This part I'm not so sure about. There are various hypotheses around regarding this. What constitutes a 'scientific rational' supporting a hypothesis is a rather subjective assessment.
I'm not so sure about this either. I have read of studies that indicate otherwise, but I don't have them at hand to cite. Further, it's difficult to determine whether it's the change in calories, the change in foods eaten, changes in activity level which caused a weight reduction, particularly given that those factors might well be interacting - i.e. a healthier diet with the same calories might either change the basic metabolic rate or it might change the subjective feelings of well-being leading to a higher activity level which results in a higher metabolic rate.
Bottom line, while I agree the idea that eating different foods while maintaining the same calorie intake and losing weight isn't scientifically verified, I don't think you can assume that everyone who has had an experience like Dumbledore related is necessarily mistaken about how many calories they ate either.