It seems you're mixing things up. "State" in this context doesn't mean caching results. "State" in this case means that your code has internal state that you can't control, thus your components behave unpredictably depending on factors you can't control.
Picking up your caching example, what would you say if your HTTP cache either returned your main page or some random noise in an apparently random way, even though you're always requesting the exact same URL?