I came across this story earlier today, and I was nonplussed by the title: "Belief in Reincarnation Tied to Memory Errors." After reading the story, I realized that 'belief in reincarnation' here meant belief that one had been reincarnated as some particular person, as opposed to the belief that people qua souls/atmans are reborn in different bodies commensurate with their latent karma.
It's a standard assumption in the Hindu literature with which I'm familiar that an individual is not and cannot become aware of his or her past lives–at least as long as he or she continues to have an embodied existence. Buddhism is a bit different, but even there it is only an Arhat (one who has achieved full enlightenment) who can become aware of his past lives. The point here, outside of the ambiguity in the article's title, is that even within the traditions I'm aware of which accept the occurence of rebirth in some form, there's still not much reason to take most people's claims about the particulars of any previous births seriously. Even from within those traditions, one should probably put as much credence in such claims as a typical Catholic should in the divine origins of the Virgin Mary grilled cheese sandwich.