I believe you're left with a situation that intrigued Joseph Campbell - is the appearance of a motif amongst the Amerindians that parallels almost exactly one from Mesopotamia the result of cultural transmission or spontaneous production from the unconscious psyche.
And his answer?
Well, it depends on which books you read! In some of his books he's definately pro-exchange, in others he is not. I like to think of him as a reluctant Jungian.
I like to think that similar archetypes arise throughout the world independently, but that this similarity allows the exchange of religious ideas and symbols - one facilitates the other.
It is easy to explain common motifs away by acculturation and exchange - but when one suddenly dreams of something 'archetypal' with no clear origin for that thought save one's own mind, then this surety disappears. For instance I once dreamed that I was chased in a forest by a horned creature, stabbed, hung, dismembered and resurrected. At the time I'd never heard of shamanism, yet these are clear shamanic symbols. If such images can arise of their own accord in my mind then why not in others.
if the pyramid should arise in the mind of an Egyptian - why not in the mind of a South American Indian?