That's only half of it. It rains in the Amazon so much also because of the Andes pushing air from the oceans up where it condenses. You can see this happening in Hawaii in real time everyday where one side is a lush jungle and the other side is Mediterranean style desert similar to southern California and there's no way it's purely from the jungle. It's mostly coming off the ocean
Trees make their own rain, it’s a known thing, and if the moisture was only from the ocean then you’d expect it to rain to the west of the mountains not to the east.