Nor actually do I attempt to offer metaphysical or mathematical theories about how such uncanny parallels can come about. I'm just not very mathematically minded. I work with models of consciousness instead.
The basic fact I perceive is that indigenous and traditional folks, and moderns such as ourselves in certain circumstances, experience a state of permeable consciousness, where the Cartesian separation of knowing subject and pre-given object "out there" vanish. The self is experienced as the cosmos in this case, where it emerges as perfectly reasonable that the waters should be vital with sentience and have their unique spiritual essence. Not to mention be capable of communication with us. Thus, it's not too surprising that the ancient Greeks and contemporary Amazonian peoples have parallel mythologies. After all, we're all in this living cosmos together from the perspective of permeable consciousness, not the weary inhabitants of a dead, mechanical universe as most moderns experience themselves.
Even the best science fiction devotes itself to reanimating the universe. NO ONE really likes the Cartesian model of consciousness. We want to be alive in a living, vital cosmos filled with intelligence.
Okay, that may have been a little long-winded, but I needed to establish my basic way of thought here.
Perhaps you have something to offer about the explanatory power of parallel universes in this case?