If the child had been raised as a "devout Christian", then he would of course self-censor such impressions or memories as being not his own, since, of course, under Christian doctrine such things are impossible.
Being a "devout Christian" implies that lots of possibilities are energetically closed off or filtered.
One of the points made in the story is that the parents hadn't tried to indoctrinate this boy in any belief system (scientific materialism, atheism, skepticism, rationalism, Communism, Biblical fundamentalism) that might encourage the boy to disbelieve, filter, suppress, or refrain from giving voice to any of these impressions he had. He likewise hadn't been exposed to any beliefs or literature that would encourage him to conceive of metempsychosis. No visits to Hindu temples, no light reading from the Upanishads, no Joan Grant "far memory" novels, no "Tales from the Crypt".
By the way, not all Western thought would be so inimical to these parents' persuasion of their son's metempsychosis. The Transcendentalists believed that people do have an existence before procreation, and that children arrive in the world, in Wordsworth's formula, "trailing clouds of glory". In their opinion (I wouldn't go so far as to call it a tenet of faith), the souls of children came into the world having lived in the presence of the Logos before birth, and subject to the limitations, corruptions, and dogmatism of this world only afterward, so that childhood was a period of defilement of souls born pure and uncorrupted. I don't recall the Transcendentalists embracing metempsychosis, though.
The main appeal of this philosophy is that there is no God to answer to. One becomes one's own god and falls into the clutches of spiritual guides who are probably deceivers and agents of the god of this world we were warned about.