I don't know of anything in the NEC that prohibits a face-up range receptacle, and I've installed them that way and had them pass inspection.
406.4(E) goes out of the way to specifically prohibit mounting a receptacle face-up on a counter top, this would lead me to believe that it is generally allowed and only restricted in specific instances.
However, from a practical standpoint: I used to do apartment maintenance where many of the range receptacles were face-up on the floor. The surface of the receptacles tended to get completely coated with grease and dirt and dust. If the plug was ever removed, the receptacle would have to be taken apart and cleaned before the plug could be re-inserted.
-John
