Menary on Manipulation and Cognitive Processes Extending

It is very clear, to me at least, that the manipulation thesis does not depend upon
any kind of causal coupling (in Adams and Aizawa’s sense) and does not make any claims about cognitive processes extending from brains into bodies and tools.

And, I agree that the manipulation of structures in the environment does not make any claim about cognitive processes extending from brains into bodies and tools.  But, then what is the link between manipulating environmenal structures and extended cognition?  Or, if you don't like the term "extended", what is the link between manipulating structures in the environment and cognitive processes being realized by those manipulation processes?  I've been assuming that observations regarding the manipulation of environmental structures is somehow supposed to bolster the case for EC.  But, that looks to put Menary on the road to committing a version of the C-C fallacy.