I would think that a near-death experience, where the heart temporarily stops feeding oxygen to the brain, would affect the electro-chemical processes of the brain in ways hard to predict, but like physical inputs during dreaming, would cause strange patterns as the brain tried to cope with it all.
Upon resuscitation, I'd imagine there would certainly be 'unusual' memories of it, like intense dreams. *I* have had many flying dreams, and in a couple of them I seemed to 'see' myself floating.....though most were just seeing the landscape from 'above'. In no case was I near death.
I know that's not nearly as interesting a theory as 'having a spiritual side' that is not dependent on the brain, but it certainly is easier to explain!