Running when you don't feel well

I woke up feeling tired and weak this morning and I was tempted to skip my run in the name of recovery. I had read in a book about running that there are two schools of thought about training while fighting an illness: rest and recover or powering through. I chose to run and was surprised that when I reached the end of my running time (my morning training is part of a complex set of routines that, if followed to the second, allow me to make my train) I was feeling pretty strong. It's not the first time I've experienced this - a really good run after starting out tired. I didn't eat anything prior to running as I have been doing but I had an unusually carb-heavy lunch yesterday and that clearly provided enough fuel.