Are Wheeler and Clark Closet Cognitivists?

It sound like that here:

So what sort of overarching theory of the cognitive is favoured by EM theorists? As Clark (2008, 44) notes, the fact is that '[a]rguments in favour of [EM] appeal mainly, if not exclusively, to the computational role played by certain kinds of non-neural events and processes in online problem-solving'. In other words, EM theorists overwhelmingly conceive of cognition as a matter of information processing. Their distinctive observation is that, given this view of what cognition is, extra-neural factors - including the stuff of material culture - may, in some cases anyway realize the target phenomenon just as readily as neural tissue. For example, taking it that memory is, at least in part, a matter of the selective storage and context-sensitive retrieval of information, the EM theorist with a cognitive-archaeological bent might contend that information that is poised appropriately for context-sensitive retrieval may be stored in a Mycenaean Linear B tablet just a readily as in a Mycenaean brain.

Extended functionalism and implementational materiality 

Of course, not any old kind of information-processing profile will do here. To say that it would would be to fall prey to Rupert's worry about explanatory inefficacy. No, genuine cognition will be found only in a (perhaps rather small) subset of information-processing systems. (Wheeler, 2010, p. 32).

 To me, computational information processing of a restricted sort sounds a lot like the manipulation of representations, or a description of cognitivism sans the optional non-derived content condition.  This seems to me to reinforce the idea that cognitivism per se does not beg the question against EC, even though many advocates of EC and enactivism reject cognitivism.  Wheeler later drops the computational part for an extended "generic" functionalism, but that is still consistent with a thin sort of cognitivism that Adams and Aizawa have been urging since "The Bounds of Cognition" in 2001.