Like, even South Park had the courtesy to not give Mohammad a face.  

No, they did and it was censored by Comedy Central.

Parker and Stone note the contradiction in being allowed to feature a profane depiction of Jesus, while being forbidden to feature a purely benign depiction of Muhammad, but claim they harbor no hard feelings toward Comedy Central for censoring the scene, since the network confessed to being “afraid of getting blown up” rather than claim they refrained from airing the scene uncensored out of religious tolerance.