That's not written in stone either. Grigg (1987) reviewed patients at a hospital and identified a considerable number whose brainstem was totally destroyed, absolutely brain dead by all medical criteria, (hopeless cases) but scalp EEG recordings were still measuring electrical brain activity, some patients displayed sleep like brain wave patterns, yet their brainstem was just a mess of necrotic tissue. So trying to claim that if the brainstem is down, there can be no other electrical activity in the brain, as if it were some golden rule, just isn't correct.
In cardiac arrest, the brainstem, cortex, the whole brain is taken out of the equation. No blood flow = nothing going on after 10-20 seconds, the patient is dead and will stay dead unless resuscitated
A simple way (for Malf particularly) to envisage this is to think about a house and it's vital services, electric, gas, water supply etc. To make sure that all systems in the house are non functional, all that needs to be done is flip the switch on the RCD, turn the gas lever and close down the stop cock. Everything stops.