Here is the wiki page for those confused by point 3 of this summary: it seems to be a generalized version of the argument that speech synthesis is difficult to do realistically when the algorithm doing it is deaf, and that speech synthesis would be done better by some kind of bidirectional program that recognized human speech (this is partly inspired by the analogous situation with deaf people).

Is 2 really an accurate summary of the idea? I don't know of any embodied-cognition types who negate computational processes utterly (very possibly a limit on my own reading); AFAIK it's considered "insufficient", not "unnecessary." Poking around Wikipedia doesn't immediately suggest that either. What are you summarizing here that leads you to think this is an accurate statement of what embodied cognition entails?

Theme 3 is trivial for the body in the following sense: every cognitive concept is normally ascribed to whole organisms and ascribing cognitive concepts only to brains (or minds) is a modern conceptual extension. The "extended cognition" thesis (that parts of the world are also constitutive of cognition) is a little more controversial (although it's surely less controversial that parts of the world can be part of our explanations of cognition). In some ways "embodied cognition" is thus little more than a rejection of some of the presuppositions of traditional cognitive science.