Buddhism rejects reincarnation categorically.
Buddha fought with ideology of Brahmanism, like Freud fought with teaching of psychiatry. That led both of them to inventing totally new theories, which had to describe the same world and phenomena from totally new point of view. Such trick is very nice when you want to cut the ground from under feet of your opponent, but not really good if you want to describe the reality, because denying
all what was said previously, you occasionally can throw the baby out with the bath water.
The same thing, IMO, happened with Buddhism. In their polemics with Hinduism they deny existence of
any material carrier which can keep the memory about previous incarnations (otherwise they would have to accept the existence of Atman, which, according to Hindu teaching, is the "self" which reincarnates.) Acceptance of Atman, the core concept of Hinduism, means acceptance of the whole teaching which Buddha wanted to destroy. That's why they are so categoric with respect to this topic.
However, if one decides to think himself (but not just reproduce texts written in polemics with ancient opponents, like many religious Buddhists do), he will face the question: how the information from a lot of previous lives can be transferred to current living being without physical carrier? This question can be easily ignored by those who are not good in physics, but for people with scientific mind and scientific background it is clear that there should be
some carrier.
This carrier needs not to be the same object as Atman, described in Hinduism, but statements about total absence of such carrier are also not correct. Such "physical" approach makes things much clearer and easier, and allows to focus on investigation of real nature of the phenomena, rather then on quotation of ancient texts. And this approach is totally in lines with Buddha's teaching.