The man in the Man in the Maze symbol has a name, I’itoi. He is the creator god in the cosmology of the Tohono O’odham and Pima Indians and the image appears frequently in their crafts. Interestingly enough, the symbol in this particular image is on the wall of the Catholic Mission San Xavier del Bac.
It would seem that the story of I’itoi would represent a conflicting view of creation to that of the Catholic faith, but then the Catholic church has historically been quite good at integrating into their own religion (at least locally) the existing religious symbols and ideas of the peoples who they convert to Christianity. (The Celtic Cross, for example, predates Christianity and had pagan myths attached to it long before it became integral to Catholicism in Ireland.)