Shorter Sutton and Menary

One nagging concern I've had about the Sutton, et al., and Menary "Holy Grail" papers is that they do not seem to me to be all that interested in the claim that cognitive processes are realized by (or supervene upon) processes in the brain, body, and world.   This, however, seems to me to be one of the least problematic ways of stating the hypothesis of extended cognition.  I worry that the discussion has somehow gotten off track.