There are two separate things here. One is diabetes. For that, you just do whatever works. If you can cut basal insulin and manage that way without carbs, it’s fine.
The other is the running part. For that, giving your body carbs is the best thing from a perspective of fueling the exercise.
So when I said you should have carbs, it wasn’t for the diabetes, it was for the running part. 
There is a level of exercise where you can use all fat metabolism. And then as you speed up, you are increasingly using more carb metabolism (muscle glycogen, and glucose in your blood and what you have recently eaten).
Anyway, I was just referring to you as a runner, not as a diabetic runner. And I think that is the best way to go. That is always my goal, every run.
This is a very simple explanation.
how-does-my-body-fuel-exercise
And this one is a bit more complex:
RER-how-exhaled-air-tells-us-our-fuel-source
Anyway, I am not trying to talk you out of something that works for you as far as BG management. I am just talking about the ideal way to fuel your run as a non-diabetic. As you increase your intensity, you increase the carb requirements. That’s when you really want to start taking in carbs as a part of the run.