I would like to personally thank you for posting the post that you did. I am a researcher; I been doing it for about 60 years. I have studied many different subjects over the years. Some of the research covered reincarnation and life after death. Which, I have found fascinating to say the least. Much of what has been discovered could not be posted here for good reason.
My problem with this -- we'd really have to make sure these children didn't see something on TV or over hear someone talking about all this. I'm not saying I am doubting it completely, but you have to rule out the obvious.
As a mother, I would definitely research this if my really young child started talking about this stuff, though. It would blow my mind. Can you imagine -- proof of an afterlife? Proof of reincarnation?