I run every morning at 5:30 and definitely on an empty stomach. I have had 0 problems doing this. I have a super quick shower (5minutes) afterwards and then I eat a very good breakfast. The few times I have eaten and then tried cardio, it just doesn't work out for me. I feel sluggish and slow and unmotivated. If I had to eat something before the workout, I would probably choose 10-15 raw almonds.
I think it is really important to do what works best for you. You will hear differing opinions about different topics. In the end, if your system is working than keep it up!

But I feel good about at least putting a little something into my system - but there's no way I could eat more and not get sick or uncomfortable.