I think this guy is onto something. But it isn't just a no-carb diet. That is a fad and in the long run tough to maintain. But what he is onto is actually what has been preached at us since we were kids: a balanced diet. Fats, carbs, proteins all working together. We usually encounter health issues (over/under-weight, blood pressure, die-beetus, etc.) when our diet gets out of balance. Eat real foods, and a large variety of foods, and you can absorb the occasional chocolate cake or cheese cake or coke with dinner or whatever the case may be. I am a firm believer there is no magic bullet other than restraint and smart eating and upping your activity level. That is why I think Weight Watchers has consistently the best program out there if you have to have a program.
To go further into this, as frank pointed out our progenitors adapted to a wide variety of diets, but they also imbued in us as a protection mechanism the propensity to add weight (read: calories or energy) in times of plenty to help carry us through times of not-so-plenty. So basically the fat survived to mate over the tough winter, the skinny died and may have been a convenient meal, who knows. But the genetic makeup is generally one to add weight easily. And now, since for the vast majority of humans we live in a permanent time of plenty it is not strange at all that we tend toward the bigger side.
Add to that the fact that we put the most work into developing the infrastructure to produce the foods we needed and wanted. So go back 150-200 years and processed sugar was generally a luxury, and a cash crop, and grain was only available if you could farm it or trade for it, and nowhere near as easy to get and process as vegetables, which took all of picking it and eating it to get at the goods, and so these (grain, sugar, etc.) became the focus of agricultural advancement. Meaning they went from relatively expensive/rare to common and cheap, flipping places with vegetables from 150 years ago when everyone had a veggie garden and a root cellar or similar and could produce their own veggies, or someone else did we could trade with, or trade money for, so veggies tended to be cheap.
Now it is reversed, and providing fresh vegetables, which do not shelve well, is expensive. So our diet is largely a product of advancement and progress, and the world now generally eats cheaply. But what they eat tends to be a reduced variety compared to 150 years ago. And so our genes to add fat stores are doing their job as we reduce our own physical work loads or need to perform physical work, and add in cheap high-calorie-dense but low nutritionally-dense foods, and as a society we get fat.
So for the average American if they simply add variety to their diet and replace the staple fast food burger with something home made or replace potatoes with veggies, and eat real whole foods instead of processed foods, their weight will tend to normalize. Seriously if we as a nation just cut portion size and that was all we did we would collectively lose weight. Replace a few burgers a week with a tuna sandwich and carrot sticks and even more weight will drop. Find variety and whole foods in your diet again and you will become healthier, and without the need for special programs or protein shakes or anything else. Just grab a glass of water instead of a can of coke and some carrots instead of chips or fries once in a while and there you go, back on the road to a healthy weight.