I get your logic, but it isn't quite right in this case. The reason is that the production of these ketone bodies that the brain can use for biochemical energy,

I get your logic, but it isn't quite right in this case. The reason is that the production of these ketone bodies that the brain can use for biochemical energy, only get produced in significant amounts once liver glycogen stores are depleted. So in a sense it's less of a passive ability and more of an active response to starvation.