"collective thought/memory" - correct. Its a theory of consciousness. Our brains are transceivers of consciousness. Just as Jung's theory of the collective unconsciousness, there is a small group of researchers/scientists that propose a collective consciousness that some people can access and believe they have lived that life.

I happen to be one of these people though I am not an researcher nor a scientist. (You might refer to me as "a nutbag" lol).