Training hungry has biological value. When you eat, the food travels to the small intestine, where almost all digestion occurs. The conversion and use of broken-down nutrients becomes a priority to the body.
In order to transport these newly absorbed nutrients to various organs and tissues, the blood vessels in and around muscle tissues constrict, while the vessels in and around the digestive organs dilate. That forces blood away from muscles toward the digestive system, minimizing oxygen and nutrients going to the muscles.
Imagine what happens when you eat just before you train. Digestion occurs at the same time you perform the activity. That results in a tug-of-war between your muscles and digestive system, both desperately in need of increased blood flow.