Hypoglycemia - The brain is very sensitive to low glucose levels and can't compensate by burning fats and ketones like other body tissues, resulting in a relatively rapid onset of AMS/Consciousnesses.?
The brain can use ketones as an alternative energy source. The problem is they are produced in sufficent quantities in order for them to power the brain for long.
So your answer is partially right.
Hyperglycemia - A good portion of the brain (not all of it) can transport glucose into the cells independently of insulin and as a result, in an acute time frame the brain can compensate for a decent period of time. Usually until the buildup of ketonic acids causes a metabolic acidosis.
The issue is not specifically ketones, as the brain can use them. But ketones are produced by the breakdown of fatty acid, which the brain cannot do.
The main problem with hypoglycemia is membrane (both cellular and mitochondrial) functions. (Na, K, H etc transport and permiability.)
Also, does failure of the brain without insulin ultimately occur because the brain doesn't have insulin, or because the supporting body tissues/organ systems linked to the brain can't function without insulin??
Yes, for both reasons.
The Glut 1 receptors in parts of the brain require insulin, without it, they will fail.
As well, metabolic (hormonal and catecholamine) signalling alters the function of other organs. Which will fail without insulin as well as ultimately fail from inability of homeostasis trying to compensate.
Ultimately, both myself nor my partners are fully wrong or right. The brain is so complex that we are both right, the brain doesn't need insulin, but in the end it really does?
I think you will have to settle for both being pertly right and partly wrong.
The brain is a rather complex thing and 1 or 2 mloecules and biochemical processes do not accurately describe all of the interrelated functions.