I think it's hard to find "true experiences with the supernatural" credible because even if the person believes it happened: humans make for awful sensors. They might feel warm when they're cold or vice versa. They regularly see things that don't exist. More than half of us appear to be some kind of moron.

And why would a ghost be unmeasurable? Why could something be truly ethereal when everything ever measured or recorded is not? Plus, the seemingly random limitations on any sort of fairy, ghost, or deity make it pretty much dead in the water as far as theories go. Imagine this, you're some kind of land-god of wealth and/or stealing and potentially eating babies. But you go years or decades without fulfilling your own theme or being seen by humans? And you can't leave your territory as defined by human maps like you need permission from city councilmen?

All of this on top of the belief I hold that life is a culmination of billions of tiny mechanisms that, upon systemic failure, result in something akin to gears no longer turning in a clock means: either machinery and electronics all have "souls" or humans don't. Where would you draw the line? Do waterfalls have souls? The grand canyon? Dogs?

So pretty unlikely, all things considered.