I don't know if I'd call the peaceful conquest of the Aztec Empire a "miracle." For, it has really turned out to be a curse, something Southwest America is suffering daily. The Aztecs believed Cortes was their fabled serpent god, Quetzalcoatl, and bowed down and worshiped him. Quetzalcoatl was, of course, Lucifer's ancient appearance to them, in the form of an Adamic (White) man, with a beard.
As for "Our Lady of Guadalupe," with all due respect, that is a shrine to the Aztec Earth goddess, Tonantzin, using a Catholic veneer. The Guadalupe shrine is at the exact same location as the worship of Tonantzin: Tepeyac. The syncretism of Aztec paganism, and Catholic rites and icons, is deep and pervasive. Things like the Dia de (los) Muertes - worship of the dead - demonstrate just how deep the syncretism is. Are the Mesoamericans better off as "Catholics"? Of course. But the faith of the majority of them is not the same as Biblical Christianity.