Tend to agree with Nevadaref on this...the literal definition of "over" includes "used as a function word to indicate position on the other side." Hence, the other side of being face-down on the floor is being face-up.
Having said that, I openly admit to often being too quick on the whistle when I see the face-down player beginning to roll to one side or the other. Partners, coaches and evaluators have all commented that I need to hold just another second or two before going to the travel call.