I have to go with HB here. There is no physical reason that CF should impose any rotation around the longitudinal sweet spot axis.
My take on this is that the face is mostly squared by the rotation of the RFFW and the LAFW. The right (pitch) elbow can only be maintained so far into the down swing, and when RFFW rotates back on plane so does the club face.
Here's a Nesbit paper where the "gamma torque" that opens and closes the face is discussed - among other things
http://www.motionanalysis.com/pdf/2005_nesbit.pdf