There's a staggering amount of "reliable" evidence -albeit anecdotal, to suggest the mind can exist independently of the brain- you only have to look. More recently the view that we might be living in a simulation is suggestive of the fact that we exist as a materialistic avatar controlled and interlinked by a mind/consciousness. There are veridical accounts of NDe's and even quantum entanglement allows for the existence of forces that cause actions on "objects" in a non materialistic way-so I don't see why apparitions of some or even different states of existence are a problem?
Reliable anecdotal... that's pretty much an oxy-moron.
There's a reason that science runs double blind experiments with control groups etc.
Eye witness evidence is the least reliable evidence, there's tons of investigations into just how poor it is. People have terrible memories, that fill in details all the time. I have a very solid memory, my earliest memory, of me when I was about 3, in my buggy on a really rainy day, with the rain cover on.
Only problem is, I know that it's false. It's almost certainly based on a real experience, but I know it's false, because the steps to our door and the path, are from when I was closer to 6/7 years old (extension to the same house). People can be convinced of virtually anything, memories aren't fixed, but flexible, and can be manipulated. There's a reason why the likes of Derren Brown can have some much fun at our expense.
Hypnosis in general is a good way to see how the brain can be manipulated too. I was never sure if it worked, fairly sceptical in truth (science degree). Got called up to be part of a stage hypnosis show (so it's not all plants!). Played along for the most part, or at least thought I was playing along. He then told us that when he blew his whistle the chair would feel really hot. I was getting bored by then and decided I wasn't going to react. He blew the whistle and my body took over. I can't say I felt the heat, but my body sure as hell didn't want to stay sat down. Next up he gave me a book, told me to start reading and it would be the funniest book I'd ever read. It was a passage about near death experiences, but I could barely get through the first sentence before tears of laughter were running down my face.
The human brain is a million miles away from infallible, and can be manipulated (deliberately or otherwise). Anecdotal is not reliable. Years ago people used to see witches flying in the sky, then it was updated to UFO's, as our fantasy developed, how many people see witches on broomsticks these days? Have they all died out, or just fly easyjet?
I did have a little chuckle