Why should I be concerned if a leap of intuition led to the conclusion things falling and movement of the planets were caused by the same thing?
Because if you accept it without proper argument (and that is what I take "conclusion" to mean) you're not doing science. It would not adhere to the scientific method. I think you should stop trying to lecture me about it.
Doesn’t matter how a hypothesis was postulated, what matters is that it can be tested and falsified.
Indeed, you can take another stone and it will also drop to the ground: Testable, falsifiable. Things, indeed, do fall down. Nature indeed replenishes from the sacred site, that's also testable and falsifiable, they probably did test it at some time and then went "ohfuckohfuck". As one can be directly observed it's physical, as the other can't it's spirits. Further investigation then could conclude that the spirits are actually tiny stuff you need a microscope to see, but the people don't have microscopes also that wouldn't mean that it's not spirits, but that spirits are tiny things you see with a microscope: Why change the term?
This not changing of terms also has precedence in western science btw: "atom" means "undivisible thing" (from Ancient Greek ἄτομος, "I cannot cut"). Does it mean that physicists are not able to tell neutrons, protons and electrons apart?
Nothing, whatsoever, about not even having a concept of materialism precludes one from employing the scientific method. Science is not a set of beliefs or insights, it's a method. And, as you yourself said: Everyone can do that. I'm saying: Just because a tribe didn't do as much science as Europe from Antiquity to Modernity you shouldn't assume that they're talking mumbo-jumbo. They may know shit about quantum mechanics they certainly know a lot about how their environment works.
Another example would be the agriculture of Australian Aborigines, which is so far-out when it comes to techniques that it didn't register as agriculture to the settlers, they thought Aborigines are hunters and gatherers. Sure, they hunt and gather, but within an environment they had shaped such that stuff grew where it was convenient, and animals lived were they were easy to hunt. You don't get to that level of ecological engineering without understanding things and interrelationships, that means they did science, even if your tunnel vision can't recognise it.