The body can produce the amount of glucose it needs through converting proteins using Gluconeogenesis. Dietary intake of carbohydrates/glucose is not necessary.
I don't think you went over that medical summary I provided: Fatty acids do not serve as fuel for the brain, because they are bound to albumin in plasma and so do not traverse the blood-brain barrier. In starvation, ketone bodies generated by the liver partly replace glucose as fuel for the brain.