Sorry, but this is a completely shocking article to me. First in it's immediate dismissal of any formalism inherent in natural language, but also with the ease at which he dismisses the proposition without any real consideration.
If we learned anything from Chomsky, it's that the underlying grammar we are born with is both instinctual, and follows formal rules. To say differently is literally, demonstrably false. Irregular verbs, for example, aren't learned in the traditional sense, one must actually unlearn the formal rules. Any child that tells you she "swimmed" all afternoon is using a more formal version of English than you do.
The idea of a natural language programming language is flawed, but not by formalism. It's flawed by the evolutionary nature of natural languages. That is, the very people that he states "are no longer able to use their native tongue effectively," are probably using a new dialect that shares a common ancestor with his more "traditional" usage.
Many people in this thread are talking about the inability of plebes to express what they actually want. This is a fair point, but not a problem with language specifically. Communication tools would need to be employed by a computer in the same way as humans use them. E.g., a simple ambiguity checker could work wonders here, as it does between humans when someone you are talking to simply says, "What did you mean when you said you 'realized you forgot your phone at the train station'? Did you forget at the train station, or realize at the train station?".
What IS a problem, however, is Quine's indeterminacy of translation. That could pose serious hurdles that may be insurmountable, however, we still have effective communication between humans, so it's simple to see how this may only be a theoretical problem, rather than a formal one.
This subject should be under the purview of analytic philosophy and linguistics, not mathematics or computer science.