I nearly always work with “Limit selection to visible” turned on. If it is turned off, or the viewport mode is set to wireframe then the centers shows, otherwise they don’t. Though on occasion the centers have shown at other times and it confused me. I’m on 2.77a and I don’t know if I might be holding some legacy memory from earlier versions. But if the centers are off, then any selection method just needs to touch the edge of the face to select it.