"Another problem with the claim that Chomsky’s theory of language “is being overturned” (as if it had ever been accepted, which is not true), is that it’s not clear what “Chomsky’s theory of language” refers to. He has proposed a succession of technical theories in syntax, and at the same time has made decades of informal remarks about language being innate, which have changed over the decades, and have never been precise enough to confirm or disconfirm."
There are a bunch of ideas that are more core and strongly supported (language is innate) which you use to explore more tenuous ideas about what the implications are and how they specifically manifest. Linguistics is an extremely nascent field compared to other sciences, Chomsky calls our stage of understanding "pre-Galilean", no one has claimed to have solved the basic questions yet so it isn't surprising that anything other than the core ideas are in constant flux. I haven't seen a good counter argument to the core ideas of universal grammar (or the minimalist program) and to refute an idea you need to actually present a counter-argument not simply say some sub-hypothesis has been refuted in the past so every fundamental idea has been refuted.
The SciAM article you linked doesn't understand the arguments Chomsky makes when "refuting" them (e.g. they erroneously say that superficial differences between languages show that there is no universal grammar).
I thought I read an article one that some very untouched tribes (ala amazon?) have fundamental different ways of communicating that undercut Chomsky's notions of universal grammer. Which the SciAm article glances on, but doesn't really go into any depth.
That's Piraha and Daniel Everett's work. Even assuming the results are correct (that Piraha doesn't use recursion) that doesn't demonstrate anything relevant. What you want to show is that Piraha people don't have the ability for recursion (i.e. they are an example of people without this innate language faculty), not that they don't apply it. I don't think anyone believes that if you take a Piraha newborn to New York they wouldn't learn English.
"Another problem with the claim that Chomsky’s theory of language “is being overturned” (as if it had ever been accepted, which is not true), is that it’s not clear what “Chomsky’s theory of language” refers to. He has proposed a succession of technical theories in syntax, and at the same time has made decades of informal remarks about language being innate, which have changed over the decades, and have never been precise enough to confirm or disconfirm."