I think the weak version of it is that people feel they need some explanation of why they think "they" can see something looking out their eyes.
A weaker version that tries to be stronger is Penrose's argument from The Emperor's New Mind which goes along the lines that "A machine can't do math because of those problems Gödel pointed out, but I can prove theorems so I'm not a machine, I'm a thetan [1]" Penrose is not consistent or complete or able to prove he is consistent or complete so I don't think Gödel has anything on him -- and there is no problem building a machine that can prove some theorems even though you can't build a machine that proves all theorems but Penrose can't prove all theorems either.
I'm also skeptical about anything involving sleep, anesthesia and such because so far as I know you are able to respond to stimuli when you're asleep and may very well be "aware" of them but what's clear is that you're not writing narrative memories, whatever LRH says.
[1] https://www.scientology.org/what-is-scientology/basic-princi...