Speaking from my personal experience to counter this, I run in the mornings up to 1 hour on an empty stomach. While I don't follow one diet, a larger portion of my food is carb based.

I follow TFTNA (Training for the New Alpinism) and Uphill Athlete (Steve/Scott's new book) training regiments that Parent mentions.

They do talk about retooling your body to use fat reserves more than carbs. While I'm sure the evidence shows that keto diet might make this switch faster and easier, someone on a non-keto diet (carb based) can also do this.