Focus on Haugeland’s trip to San Jose. In the actual case, his body is embedded, for it is tightly coupled with the road. To be embedded with something is to be coupled to it. It is possible, however, to imagine a counter-factual case in which he has an inner mental representation of the route to San Jose. Imagine, for instance, that Haugeland is able to find the way to San Jose by memorizing the number of steps and turns that he must take in order to get there from a certain starting point. In this imaginary case, his body would be unembedded, for although his body would be causally interacting with the road, it would not be coupled with it. Strictly speaking, in this imaginary case, the road does not play any cognitiverole whatsoever in Haugeland’s finding his way to San Jose. Now, advocates of EMH take the actual case to be fundamentally different from the imaginary case. A&A, however, would see the cases as fundamentally similar. Because they conflate coupling with mere causal interaction, they would emphasize a superficial similarity between the embedded and unembedded cases: in both, Haugeland’s body causally interacts with the road.Now, I see that A&M want Haugeland's original case to count as coupling and extended cognition, but the new case not to count as coupling and extended cognition. So, what exactly is the putative difference between mere causation and coupling? A&M don't say. Could it be that when X is a causally relevant factor that contributes to the success in some task, then X is coupled, hence part of the cognitive system?
But, by this account, we are coupled to the sun when we read outside or to oxygen when we solve math problems. Rupert talks about the sun case in his book, and probably elsewhere. So, the account of coupling on offer here seems to me to be of no help.
Second, this account seems to me not to distinguish between cognition and behavior. It is behaviors that enable success in tasks, with cognitive processes only being (perhaps) among the causes of behavior. If one takes all processes that contribute to the production of (successful) behavior to be cognitive, then that conglomerate will be extended.