Generally people discussing “low carb diets” really mean managing blood glucose/insulin spikes. So high glycemic carbs, refined sugars, refined carbs.
Not all carbs are created equal when we talk about impacts on blood glucose and/or the liver.
It's likely that beside the rice and maize, most of their carbs come from vegetables. It's one of the reasons why high-performance diets are usually heavy on the broccoli!
What seems consistent is that both diets high in whole grains and high-fiber diets in general have some heart health benefits. My guess is that refined+enriched flour in a high-fiber meal is not much, if any, worse than whole flour in a medium- or low-fiber meal. Those pastries and chips between meals, on the other hand...
It sounds logical, but I don't know if it's really useful if you're not diabetic.
Edit: the book is called "The Personalized Diet."
It’s probably very useful to measure what spikes ones insulin so the individual can avoid those foods.
For example I know whey, a protein powder with zero carbs/sugars will spike my insulin (because it knocks me out of ketosis). Probably not a bad idea for a body builder who wants to replinish their muscle glycogen stores after a hard workout, but not going to be necessary and over long term even harmful to someone who isn’t depleting their muscle glucose/glycogen stores. In fact protein that can’t be used is generally converted into glucose which when not used is store in fat cells.