The tub should be set in a mortar bed, and the only screws I remember going into the surround are along the top edge. Kohler is quite specific about where the studs should be when building.
If there is some reason not to use full dimension framing, I would at least use furring strips to keep it off the concrete.
You must use pan head screws around the flange edge or it will crack when the screw is tightened. Lath screws are preferred, as the heads are thin and do not interfere with the overlaying wallboard.