> when linguists actually went looking at the variation in languages across the world, they found counterexamples to the claim that this type of recursion was an essential property of language. Some languages—the Amazonian Pirahã, for instance—seem to get by without Chomskyan recursion.
This is a pretty thin counter-example. A Christian missionary who became a linguist claimed that the Pirahã language had recursion. Then he later claimed that it did not have recursion. Linguists went down to study the Pirahã and found out that his first reports of Pirahã being recursive were correct, as they observed recursion in Pirahã language when they were there.
The authors return to this language spoken by less than 400 people later on:
> Chomsky defenders have responded that just because a language lacks a certain tool—recursion, for example—does not mean that it is not in the tool kit... makes Chomsky’s proposals difficult to test in practice, and in places they verge on the unfalsifiable.
Recursion in languages has not been falsified - it has been found in all languages, including Pirahã.
I think you're giving Dan Everett (the person you're describing) a short shrift here.
He says that his initial pro-recursion reports were attempting to fit Pirahã into the standard Chomskyian UG framework of the time. However, as he learned the language better, he started to realize that it didn't really fit and he was seeing the things he expected to see. For example, he initially described -sai as a nominializer (an "adapter" that lets other parts of speech be used in constructions that expect a noun). His later reports argue that it's actually not a nominalizer, but marks old information ("As you know Bob").
As far as I know, there is not actually a ton of non-Everett data on Pirahã.
The most well-known paper that disagrees with Everett is probably Nevins, Pesetsky and Rodrigues (2009), which reanalyzes Everett's published work. They start with a list of properties are are supposedly unique to Pirahã, and claim that many of these show up in familiar languages. However, I don't find that paper completely convincing. For example, Pirahã possessives can't be embedded: the equivalent of "John's brother's house" is ungrammatical and needs to be rendered as "John has a brother. The brother has a house." NPR argue that German has a similar restriction. This is true, sort of, in that "Hansens Auto" (Hans's car) is grammatical, but "*Hansens Autos Motor" ("Hans's car's motor") is not. However, this occurs because of a totally unrelated restriction: you can say something like "Hansens Vaters Frau" (Han's father's wife) because everyone involved is animate, and there's an alternate route involving "von" for embedding other kinds of possessives (as in "the motor of John's car"). Pirahã, as far as I know, does not have any possessive embedding at all, which does make it different from German.
I'm also not sure that cherry-picking individual examples from many other languages successfully refutes Pirahã's exceptionalism. German may prohibit embedding in this circumstance and Hindi in that one, but surely the interesting part is that Pirahã seems to prohibit it everywhere. As an analogy, I know people who do not write with their left hands, and other folks who don't write with their right hands. However, this doesn't imply that hands aren't involved in writing at all.
Realistically, this debate is going to be hard to settle without some more data. Unfortunately, Pirahã is said to be impossibly difficult to learn and there aren't a ton of native speakers wandering around universities. There is some data kicking around from another Australian language which may have similar properties, which might help.
There is no consensus about this question. Both sides clearly have an ax to grind. Everett knows the language best, so I'd lend more credence to his judgment. Regardless of the answer, it only means that Chomsky's theory that everything is about recursion may or may not have been falsified, not that it is a good theory.
This is a pretty thin counter-example. A Christian missionary who became a linguist claimed that the Pirahã language had recursion. Then he later claimed that it did not have recursion. Linguists went down to study the Pirahã and found out that his first reports of Pirahã being recursive were correct, as they observed recursion in Pirahã language when they were there.
The authors return to this language spoken by less than 400 people later on:
> Chomsky defenders have responded that just because a language lacks a certain tool—recursion, for example—does not mean that it is not in the tool kit... makes Chomsky’s proposals difficult to test in practice, and in places they verge on the unfalsifiable.
Recursion in languages has not been falsified - it has been found in all languages, including Pirahã.