Sugar cane was the product of the New World, as was corn and many other products we take for granted. Before then, people ate very plain food. If they could afford it (and very few could. Remember, this was the time of feudal kingdoms and most people lived in absolute squalor), they used honey to sweeten their food or salt to flavor it.
The diet DOES allow for fruits and grains as well as meats. In the EARLY stage, you are supposed to cut the fruits and grains out and then slowly add them back, being aware of how each food affects you. If you have a bad reaction to a particular food, you may have an intolerance and should avoid it. In the end, you should be able to eat a normal, but healthy, diet. A diet rich in fruits and vegetables, with low-fat meats and seafood, whole grains and nuts and very little sugar. What would be eliminated permanently is processed foods and junk foods.