This is not a complete explanation. The most important factor is that Americans just have more resources than most humans in history. Transfer any but the absolute poorest Americans to anywhere on earth, at anytime in history, with their current income, and they'll be just as well-fed as they are here and now, even if the local farmers are driving oxen.

Another way of stating this, is that edible commodities are just as fungible as all other commodities. If Egyptians could afford to purchase enough wheat to feed themselves, they would.