The point of the ecological turn in cognitive science is to show that there are deep consequences for our conception of cognitive agents once we consider their embodiment and embedding in an environment. The whole purpose of Adams and Aizawa’s arguments is to deflate those consequences, but you can’t do so just by assuming that agents are cognitive independently of their environmental embedding. (Menary, 2010)This comment I think confuses what is at issue. A&A think it is fine to consider the embodiment and embeddedness of cognitive agents in environments. That's the whole point of our concession to Sutton, et al., for example, and our point in the early pages of The Bounds of Cognition, that no one (short of Leibniz) doubts that cognitive agents are causally embodied and embedded in an environment. This is the deflationary side of our view.
What we resist is not looking at brain-body-world interactions. What we resist, among other things, is the claim that the same theory of cognition that applies to intracranial cognitive processes also applies to transcranial causal processes. We resist what I have sometimes called a "fractal scaling" approach to brain-body-world interactions. This is the idea that we have one and the same processes occurring at different scales of nature, in just the brain alone and in brain-body-world. This is to resist the more familiar version of Clark's EC according to which what is going on in Inga's brain is roughly functionally equivalent to what is going on in Otto+notebook.
And, yes, there are versions of EC that abandon the fractal scaling idea and say that the intracranial processes do not have to be like the transcranial processes. But, then what is the basis for saying that both are cognitive? What is the advantage to cognitive science of doing this? It would appear not to be some deep theoretical unity. What is the advantage or theoretical insight in claiming that intracranial processes constitute cognition of one sort and transcranial processes constitute cognition of another sort? Maybe, instead, it is just loose metaphorical talk.
Note that we do not just assume that agents are cognitive independently of their environmental embedding (where this claim is interpreted synchronically). We have drawn attention to certain discoveries in psychology that provide a principled basis for saying that what takes place in the brain is plausibly construed as cognitive and is qualitatively distinct from what goes on in brain-body-world systems. See, for example, section 4.2.1 of The Bounds of Cognition. See much of the discussion in Chapter 9. In chapter 9, for example, we discuss how it appears that agents can perceive perfectly well despite being completely immobilized by neuromuscular blockade. As I've mentioned before, Gangopadhyay has written a very detailed empirically informed critique of Chapter 9. She sees that there are empirical arguments to be met.