That kind of thinking suffuses their culture. It is a premise to how they engage with their world. Short-term, "I can burn this down if it serves my immediate needs," thinking is inimical to the traditional way of life of Amazonian tribal societies — or at least the ones with which I've interacted. "Cut it down and turn it into money" is, necessarily, a new phenomenon, since "money" wasn't even a thing for these people until we introduced it to them.
So, yeah. It is, in fact, rather like Avatar, your snark notwithstanding. You can dismiss that kind of thinking as animistic, primitive, or whatever else you want, to your heart's content. But denying its existence to someone who's spoken with these people, and seen the sincerity and reverence with which they hold those beliefs, is ... well, it's very reductively Western, for starters.
EDIT: It's also patently absurd to call that kind of thinking "short-term" in light of the clear-cutting, slash-and-burning, &c, that so many people there commit these days, just to get by — let alone to call it more short-term than the ways people engage today. That makes absolutely no sense to me.