I beg to differ. One can not rule out that whatever had brought civilization to the jungle
wasn't
cultural diffusion.
How else can you explain that no great civilization is to be found in that big huge Brazilian jungle compared to the Mesoamerican jungle? Also take in mind the proximities to the ocean and sea port capability. The Mayans had the sea. Along the Andes big civ starts mainly along the coast and there are legends that civilization came from the sea. The exception though being the bizarre Puma Punku pyramid way up on the altiplano.