I wasn't impressed with the article's arguments. Their basic argument is similar to the don't eat anything white diet. Yeah if you were to follow a don't eat white stuff diet you'll eliminate sugar and flour, but you'd eliminate those carbs in spite of their being white and not because of.
A paleo diet approach is only the premise. It then must be followed up with endocrinology and biochemistry lab work. With grains you get the problem of excess starch, and those certain lectin/gluten that cause leaky gut and celiac disease. Fructose is similar to alcohol to the liver and kidneys.