This one is a bit of a bone of contention among folks, but the fact is that what the body needs, in the simplest of terms, is glucose. Glucose is typically gleaned from carbohydrates, true, but it doesn’t have to be.
In fact, the Ketogenic diet works by restricting carbs so the body is forced to tap fat reserves for the glucose it needs. Consuming too many carbs, a problem for many people, manifests in weight gain. The body just stores it as fat in case it ever needs it. Like when it goes on the Keto diet.
Since your dog is getting plenty of high-quality nutrition, his body can break those nutrients down in whatever way is most beneficial for him. If the call is for glucose, that’s what gets served up. He just doesn’t need carbs.