We conclude that, although there are several mechanisms through which one can understand the behaviour of other individuals...
Mirror neurons do something else (R&S would probably prefer the term, more, but else is better I think)
the parieto-frontal mechanism is the only one that allows an individual to understand the action of others 'from the inside'
Let me explain what "from the inside" means, or at least provide an alternative to whatever R&S mean by it. In my "Eight Problems" paper (Hickok, 2009) I noted that I can understand the action of saxophone playing even though I've never performed the actions associated with saxophone playing. R&S acknowledge that, indeed, I do understand the action of saxophone playing, and do so without the benefit of mirror neurons. But they suggest my understanding is lacking something, namely that extra bit of knowledge that comes from knowing how to play a saxophone. So recognizing an action that I know how to perform = basic action understanding from non-mirror systems + mirror neuron-driven knowledge that hey I know how to make MY motor system do that!
In other words, mirror neurons support the knowledge of how to perform an action that one is observing -- that is, mirror neurons are part of the same old "how" stream that vision neuroscientists, and more recently auditory neuroscientists have been working on for more than a decade (Milner & Goodale, 1995). The "how" stream, of course, supports sensory-motor integration, or in R&S's terms, action understanding "from the inside". This is why you see motor activation during the perception of actions that you can perform: it is sensory-motor association.
Importantly, notice that there is no magical semantic knowledge that suddenly falls from heaven when we know how to perform an action. I can teach you a new word, glemph, and you can learn to reproduce it with your vocal tract so that subsequent presentations of acoustic glemph will activate your motor system by association. I could do the same with a sign language gesture. It doesn't take on meaning until you link the sensory-motor ensemble to a conceptual structure. So for example, I could define glemph (or the sign language equivalent) as 'the act of publishing on the topic of mirror neurons'. Now, the sensory-motor ensemble has meaning and you understand it, but does that mean that the meaning and the understanding is now suddenly coded or even augmented by the sensory-motor ensemble itself? Put differently, do you now have a different understanding of the concept, 'the act of publishing on the topic of mirror neurons' just because you have a new sensory-motor associate of the concept? No, you just know how to articulate the word that is associated with the concept.
I suggest that this interpretation of "understanding from the inside" explains every mirror neuron-related observation, does so more parsimoniously than Rizzolatti's account, and has more empirical support from research on aphasia and apraxia.
Hickok G (2009). Eight problems for the mirror neuron theory of action understanding in monkeys and humans. Journal of cognitive neuroscience, 21 (7), 1229-43 PMID: 19199415
Milner, A.D., and Goodale, M.A. (1995). The visual brain in action, Oxford: Oxford University Press.
Rizzolatti, G., & Sinigaglia, C. (2010). The functional role of the parieto-frontal mirror circuit: interpretations and misinterpretations Nature Reviews Neuroscience, 11 (4), 264-274 DOI: 10.1038/nrn2805