None of the buddhist traditions that I know of states that every (human) being is the incarnation of the same 'person'. Also, this would contradict with the scriptures, which describe many enlightened beings (who ended their cycle of rebirth).

On a more abstract level, reality could be seen this manner in Buddhism. Buddhism teaches the doctrine of dependent arising, which states that all phenomena are interdependent. As such there is no distinct/independent self or other.