Moberly
As a child I was deeply interested in the paranormal. Later on, I grew interested in time travel, so I think this mystery neatly ties those two interests together.
I remember first reading about this - the most famous case of a 'time slip' when I was 8 or so and being absolutely engrossed and intrigued by it.
I think since it's based on their own testimony, most will be skeptical of it. Of course they're not the only ones who have claimed such a thing. It could be ghosts, they could have really gone back in time, a delusion, a mistake on their part...
Personally, although I don't like to admit it I err towards skepticism, but it's still a pretty interesting case.