Actually, most of the brain's energy needs can also be met with ketone bodies, which come from fat (either stored or dietary). So it's possible that he may be running on ketones in the morning, after a night's fast.
http://en.wikipedia.org/wiki/Ketogenic_diet#Diet
That said, I agree with you that his theory is based almost entirely on speculation, and should be treated as such.
If the diet is changed from a highly glycemic diet to a diet that does not provide sufficient carbohydrate to replenish glycogen stores, the body goes through a set of stages to enter ketosis. During the initial stages of this process, the adult brain does not burn ketones; however, the brain makes immediate use of this important substrate for lipid synthesis in the brain. After about 48 hours of this process, the brain starts burning ketones in order to more directly utilize the energy from the fat stores that are being depended upon, and to reserve the glucose only for its absolute needs, thus avoiding the depletion of the body's protein store in the muscles.
If there's not enough glycogen in the liver and/or muscles and you are not getting any sugar from food, the body starts degrading your bodies' protein to convert glucogenic aminoacids to glucose, and thus maintain blood glucose levels and avoid fainting.
But if you have dietary glucogenic aminoacids, they will be converted to glucose and not your body protein.
I would adjust your comment above: "and you are not getting any sugar or glucogenic aminoacids from food"
"The ketogenic diet is not a benign, holistic or natural treatment for epilepsy; as with any serious medical therapy, there may be complications."
"Long-term use of the ketogenic diet in children increases the risk of retarded growth, bone fractures, and kidney stones. "
In other words, it does not seem that the body should be run this way long term.
Basically, your body runs on glucose. Everything else is a stop gap for you to get more glucose.
But don't forget that the body can make quite a lot of the glucose using a process called gluconeogenesis. And substances like amino acids, glycerol or products of fatty acid oxidation are used as precursors.
So, in essence - yes, it runs on glucose, but glucose does not necessarily come from dietary carbohydrates.
You can go on a ketogenic diet and eat plenty of healthy fats and some vegetable produce.