In the Abstract to the paper, Pinker and Jackendoff state: ‘We examine the question of which aspects of language are uniquely human and uniquely linguistic in light of recent suggestions by Hauser, Chomsky, and Fitch that the only such aspect is syntactic recursion, the rest of language being either specific to humans but not to language (e.g., words and concepts) or not specific to humans (e.g., speech perception).’ This lengthy paper from Pinker and Jackendoff constitutes a comprehensive rebuttal of this position, whilst acknowledging that the position has the attractions of elegance and parsimony. The rebuttal is clearly written, rigorously argued and persuasive. Though written 11 years earlier, it profits from being read in conjunction with Why only us: language and evolution by Robert C. Berwick and Noam Chomsky. At stake, among other things, is whether language evolved in the first instance to enable us to think (Berwick, Chomsky) or to enable us to communicate (Pinker, Jackendoff).
Link to paper: http://www.yorku.ca/johnsond/courses/phil3280/pdf/jackendoff%20pinker-%20lf-%20whats%20special%20about%20it.pdf
To repeat, some bloke on telly claimed that the human brain evolved as software to run our hands. Our prehensile thumbs etc are so sophisticated that they need massive software and that let to the language mutations.
In addition, Pinker and Jackendorf seem to be talking exclusively about spoken language. Written language represents a wholly different set of conceptual and cognitive challenges which transcend any primate abilities. Being able to read and write does not require any particular special physical adaptations (although writing of any sort is any amazing use of our amazing hands, either typing or holding a pen).