Ya, it is incorrect
. If you don't care about muscle loss, then feel free not to eat before or after you workout (lifting weights).
As far as cardio, I have heard some people claim that you will target fat burn quicker by not eating before your morning workout, and to this day people still argue back and forth over which is true. It will be up to you to reasearch this more and form your own opinion. Personally when fatloss is my goal, I still eat a little carb and protein an hour before my sessions.
Exercise nutrition is a continually changing field because it is relatively new and because different people's bodies react differently to things. As far as the post workout meal, well that is extremely important.