Yes, you are correct in your interpretation. After the first fast, I began to want healthy foods, and found myself with a craving for apples and fresh fruit and vegetables. And yes the metabolic rate does go down on a fast, and according to Hopinso, one of the water fasting forum's founders...
"...it is not a good way to safely and permanently lose a lot of weight because of the slowdown of the metabolic rate. In fact the average person's metabolic rate is reduced 20-25% in a 7-10 day water fast. It can take months for that rate to get back to normal." (for link see my original post)
The fasts are represented by the steep fall in the graph. The body goes into a special state on fasts, and produces something that powers your brain and gives you limited energy. On refeeding, you put on weigh because your alimentary canal fills up and you gain fluid. A 6-12 pound increase is common. Then at some point it just levels off by itself.
I did not quantify the food I was eating, so it is difficult to say, However I did try to limit quantities in the days after the fast, until my weight stabilized.
The difference between what I ate then and now. Now I have added beans, green vegetables nuts and seeds, and taken away meat, dairy, fat, salt, sugar and processed food. I am eating much more now that the periods between fasts, and find I have more energy, so I am probably burning more calories.
What would convince me that fasting works is to see a weight loss profile like this...
with definite steps, showing that the fast gave a greater net weight loss than dieting, but it doesn't happen. Well not for me anyway. I suspect the body only can adjust so much when losing weight, and also it is known that energy from food is required to make changes to the body, such as bone structure etc. There is also an issue of metabolic setpoint. I think you can't force nature, the body takes time to change.
I think a fast probably slows weight loss down. I think the best way is maybe one fast to kick start you and reset your taste buds, then exercise and healthy eating. I am not even convinced that a first fast is a good idea, because of the slow down in metabolic rate which may affect you for months.
People choose fasting because they see quick results, the problem is the end of fast weight is an illusion. You quickly regain 6-12 pounds and then you have a slower metabolic rate, making further weight loss harder.
But I agree with your observations. I am not 100% sure myself, but for me I am now hooked on this healthy eating and the gym, so I am not going to change and go back to fasting because I enjoy the state of mind that I am now in.
One other comparison, an aircraft landing. It does not switch its engines off, to maintain full control. When you are fasting, your body takes charge of your weight and slows down your metabolism. You are no longer in control, you are, in effect, gliding. When you eat healthy food, all systems are powered up and you can choose to exercise, ie a powered descent. More exercise is like pointing the nose down a little. It also feels good, being in control. Of course it would be nice to wave a magic wand and lose it all quickly, that's the illusion that fasting gives you. In reality though, you can only lose so much in a given time, and I think fasting slows you down.