Dr. Fung is actually not wrong. The resolution to the difficulty lies in taking into account the hormonal response of our bodies to the foods we eat, and the other piece of the puzzle is to revise our preconception about the direction of causality when we take the laws of thermodynamics into account.
A well-formulated ketogenic diet is a low-insulin diet, for the most part. Whether we fast or not is not always to the point; the key to a ketogenic diet is getting our carbohydrate intake low enough to avoid stimulating excessive insulin secretion. Adjusting the frequency of eating can also help, by increasing the number of hours a day in which insulin secretion is not being stimulated, insulin being the primary hormone that traps excess fat in our adipose tissue. But low carbohydrate intake is key, because it is the glucose of which every carbohydrate is composed that stimulates insulin secretion the most.
Protein also has an effect on insulin secretion, that is true. In a high-carbohydrate diet, that effect is about half the effect of carbohydrate, but in a low-carbohydrate, the rise in insulin is compensated for by a rise in glucagon secretion as well, with the net effect that the insulin/glucagon ratio (which is the real key) remains at the same low value. So protein consumption becomes much less of a concern, when we are on a well-formulated ketogenic diet.
That leaves fat, the third macronutrient, and whether our carbohydrate intake is high or low, its effect on insulin and glucagon is so minimal as to be completely negligible. This is why a moderate-protein, high-fat, and low-carbohydrate way of eating has all its beneficial effects; we can safely replace the calories we are no longer getting from carbohydrate with calories from fat. Once we are fat-adapted again (we are born in ketosis, as you may know), our bodies can metabolise glucose and fatty acids with equal facility. Amino acids (protein) are not so easily metabolised, which is why the body prefers to safe them for building muscle, bone, and other tissues, and why it only metabolises amino acids in situations of dire need.
Since we evolved primarily as meat-eaters, and since there were no refrigerators available on the veldt for most of the past 2,000,000 years, we evolved to function best on a pattern of feasting and fasting, gorging after a kill and then not eating until after the next kill. It makes sense, then, that most of our hunting would have been done while fasting, so it stands to reason that we would not have evolved to let our metabolisms drop just at the point where we would need to be functioning at full capacity. Restricted food intake, on the other hand, would signal famine conditions, and our bodies therefore developed mechanisms for hanging on to our reserves for as long as possible, to tide us over during the famine.
The upshot is that all of this does not negate the First Law of Thermodynamics—it cannot—but it rather tells us that our energy intake and our energy expenditure get out of balance because of our hormonal situation. In other words, we eat more food than we metabolise under conditions when we are growing (whether vertically or horizontally), and we eat less food than we metabolise under conditions where the body can draw on its reserves to make up the difference. As Dr. Fung likes to point out, gaining or losing excess stored fat is not a one-compartment problem, but rather a two-compartment problem.
P.S.–A high level of serum insulin not only requires the adipose tissue to store fatty acids to the extent possible (and prevents the fat from leaving the adipose once stored), it also interferes with the brain’s reception of satiety hormones. Once chronic insulin levels drop low enough, the hormones that regulate appetite begin to function properly again, making eating to hunger a reliable guide for proper food intake.