Sensible people should/would agree that clear cutting a rain forest for the sake of wood is idiotic when we consider that potential gain is greatly outweighed by the almost certain loss. If we want lumber, we can have tree farms. There's really no need to cut old growth forests or rain forests or anything of the sort. It's simply a matter of making people aware of the reasons for preservation (what we stand to learn about our own biology, medical advances etc).
Thus, while an individual would technically be free to take an ax to the Amazon, he would be risking the wrath of his community. And it's doubtful they would bother with this if serious harm could come to them as a result.
"I am not a Labor Leader; I do not want you to follow me or anyone else; if you are looking for a Moses to lead you out of this capitalist wilderness, you will stay right where you are. I would not lead you into the promised land if I could, because if I lead you in, some one else would lead you out. You must use your heads as well as your hands, and get yourself out of your present condition." - Eugene V. Debs