I think there are a couple of slips here ...

I take the following to be the commitments of those working in the extended mind framework: cognitive processes are causal processes (cognitive processes cause certain effects, presumably cognitive states and behaviour), the extended mind holds that certain kinds of coupled processes (processes that span brain, body and local environment) are cognitive processes. So it is certainly true that coupled processes are taken to be cognitive processes but this is a statement of identity.  (Menary, 2010).

I think there are a couple of slips here.

First, it's not a statement of identity that coupled processes are taken to be cognitive processes.  Coupled are processes are cognitive processes is probably what Menary means.

Second, if that's what he means, then while it is an identity statement, it is not a true identity statement, even according to EC.  Couple two pendula together. The joint swinging isn't a cognitive process.  Couple evaporation and condensation in a distillation apparatus.  The distillation doesn't make for a cognitive process.  So, it's clearly not true that coupled processes are cognitive processes.

This brings us to the claim that coupled processes of a certain kind are cognitive processes. That is, the "certain kinds" qualifier obviously disappeared from the conclusion.  Now we have something that appears to be correct, since that is a view one would have if one thought that the coupled process of the right sort is one in which a system manipulates non-derived representations in specific sorts of ways.  Menary and others see that this weak identity claims helps them, insofar as it enables them to avoid the objections that have been leveled against specific kinds of coupling.  But, it's not much in the way of a theoretical advance; instead it is a mere weakening.

And, of course, there is a lack of consensus on how to cash out the qualifier "of a certain kind".