You don't need to die to demonstrate that. General anesthesia suffices.
(FYI, for the benefit of those who have never experienced it, GA is a very different subjective experience from sleep. Even in dream-free sleep you wake up with a subjective sensation of time having passed. Not so with GA. The time you spend in GA is just completely gone. It feels like you went through a time warp.)
I've heard this a lot, so I was surprised the one time I went under GA and it felt more or less like a normal dreamless night's sleep. I remember a sharp transition from awake -> out, but coming around felt like waking up groggy after a few hours sleep. Since then I've wondered if that's unusual or if people who feel like time passed just assumed it would be that way so don't mention anything.
GA is insufficient demonstration though -- it is possible that memory recording and time keeping parts are down (there are several ways brain keeps time iirc), but other parts are working. I think there is always some electrical brain activity under GA, so something is still going on, just not enough to track time.