Even ketogenic diets will have some carbs, though less than about 20 grams per day. These carbohydrates, and protein being converted through gluconeogenesis, produces enough glucose for the brain. The rest of the body can run fine on fatty acids.
And yes, fiber, such as in whole wheat, slows carbohydrate absorbtion and is healthier than more refined foods, but the carbohydrates still raise insulin levels, which is bad for diabetics, and makes it really hard to lose weight.