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I'm no linguist, but I think they effectively used the pumping lemma, just like the canonical "there's no finite bound on the distance between declaration and use of a variable" proof for Algol-flavored programming languages. Either confirmation or pointing out my mistake would be greatly appreciated.
Yes, I think so.

I find that fascinating, because people usually assume that (a) natural language must be context-sensitive, because of ambiguities and all those misunderstandings in real world, where they forget that those aren't syntactic, but semantic or pragmatic issues, and (b) natural language must be at least context-sensitive, probably more, because look at how restricting context-freeness is (e.g. when it comes to programming languages).