I do not know if carbs inhibit the release of growth hormones, though I doubt it, but the reason why Asians tend to be shorter than Westerners is because of the diet. Asians consume less protein than Westerners, which is what causes the gross over-growth of Europeans and North Americans. Even in the West, children tend to be fed more traditional Asian diets by their first-generation parents, leading to similar size. While there is always a genetic factor in these things, it’s really the least of it. The average height of the Japanese is changing, for example, as the new generation eats a more indulgent, protein-rich, “Western”-type diet.