I'm not proposing that myself - simply commenting on Stevenson's cases where he documents such things. The article from which I quoted is this Scientific American blog post. And a while ago, I actually borrowed a copy of Stevenson's book, Where Reincarnation and Biology Intersect (which you can read about here) - and in that, he painstakingly documents many such cases.
We ought to recap who Stevenson was and what he did.
As for Chester Carlson:In 1958 and 1959, Stevenson contributed several articles and book reviews to Harper's Magazine about parapsychology, including psychosomatic illness and extrasensory perception, and in 1958, he submitted the winning entry to a competition organized by the American Society for Psychical Research, in honor of the philosopher William James (1842–1910). The prize was for the best essay on "paranormal mental phenomena and their relationship to the problem of survival of the human personality after bodily death." Stevenson's essay, "The Evidence for Survival from Claimed Memories of Former Incarnations" (1960), reviewed forty-four published cases of people, mostly children, who claimed to remember past lives. It caught the attention of Eileen J. Garrett (1893–1970), the founder of the Parapsychology Foundation, who gave Stevenson a grant to travel to India to interview a child who was claiming to have past-life memories. According to Jim Tucker, Stevenson found twenty-five other cases in just four weeks in India and was able to publish his first book on the subject in 1966, Twenty Cases Suggestive of Reincarnation.
Chester Carlson (1906–1968), the inventor of xerography, offered further financial help. Tucker writes that this allowed Stevenson to step down as chair of the psychiatry department and set up a separate division within the department, which he called the Division of Personality Studies, later renamed the Division of Perceptual Studies. When Carlson died in 1968, he left $1,000,000 to the University of Virginia to continue Stevenson's work. The bequest caused controversy within the university because of the nature of the research, but the donation was accepted, and Stevenson became the first Carlson Professor of Psychiatry.
(Both from Wikipedia.)Carlson devoted his wealth to philanthropic purposes. He donated over $150 million to charitable causes and was an active supporter of the NAACP. Carlson's wife Dorris got him interested in Hinduism, particularly the ancient texts known as the Vedanta, as well as in Zen Buddhism. They hosted Buddhist meetings, with meditation, at their home. After reading Philip Kapleau's book The Three Pillars of Zen, Dorris invited Kapleau to join their meditation group; in June 1966, they provided the funding that allowed Kapleau to start the Rochester Zen Center.
I think it's perfectly acceptable to be skeptical about Stevenson's research, and indeed about the idea of re-birth. Stevenson himself never claimed to have proved it, he simply said his cases 'suggested' it. And he did endeavour to conduct his research quite scrupulously, however, if you believe what is said about him in the same Wikipedia article quoted above, under 'skepticism', he was simply a gullible enthusiast who was hoodwinked by opportunists.
Having read a bit about Stevenson, I really don't accept that, but it's an 'all-or-nothing' proposition from the perspective of scientific materialism - one bit of evidence that such things occur, and their whole worldview is challenged. As Stevenson comments in the article, 'the will not to believe can be just as powerful as the will to believe'. (Actually it's the same thing, just pointed in another direction.)
Anyway, when the subject comes up in my infrequent talks at Buddhist Library, I always say that scepticism is perfectly fine, however I do point out that arguing against the possibility - as Stephen Bachelor does - is another matter. 'Suspension of judgement' is just that, whereas arguing against the possibility is another thing altogether.