problem with this is that it's generalising from a random exceptional circumstance.
how many children will tell similar stories that when investigated will amount to nothing of significance. this particular story is just one of those times that something appears to have something more than random connections going on, but they are still random - the reader/viewer/investigator/believer is simply applying significance to events that don't warrant it.
taking from the population of children on this planet that will have 'past-life' stories to tell, you would expect that some of them will match with real life histories - but this isn't because of reincarnation, it's just the small exceptions to the rule where, on the whole, there will be no parts of the story that match with history.
that's how i wish to interpret it anyway.