i am sorry this is not biochemistry this is made up "science". When ketosis is entered (by depleting ready carbohydrate resources) the body can metabolise fat into ketones (via the liver). The reason this myth persists is because for decades medical researchers couldn't imagine the brain running without glucose, which is a necessary condition of ketosis.
A bit of medical history: Prior to the 1920's or so, ketogenic states were commonly encountered in two medical conditions: Epileptics, and Type I diabetics.
For epileptics, a ketogenic diet was one of the few methods of seizure control available, prior to the invention of anti-epileptics -- the whole goal was to run your brain mostly on ketone bodies. It's still used in some difficult cases, although it takes a great deal of discipline and attention, as the requirements are stricter than what a weight-control ketogenic diet requires.
For the Type I diabetics, a ketogenic diet (with intake set at near-starvation levels) was the only way to keep them alive, prior to the discovery of insulin -- but it could not keep them healthy, as they gradually wasted away and either died in a state of starvation, or in a state of diabetic keto-acidosis. Once mass-produced insulin became available, the skeletal figures of diabetics plumped up, and the ketogenic diet fell by the wayside.
Unfortunately, these two medical uses of the ketogenic diet also meant that the ketogenic state became associated with disease conditions, and thus something to be avoided.