The argument seems to be "you shouldn't do this because it accomplishes the goal it was intended to". Saying don't use this pattern to hide internals because it achieves the goal of hiding internals seems dubious at best.
That would be why bulk of the article is about how you shouldn't actually want to completely hide your internals, and it's not a completely terrible argument.
It does ignore the other benefit of module-closures, though (avoiding namespace collisions). Explicitly exposing your "private" functions (prefixed with _) in the module object would be a better way of achieving what the author wants.
I had the same impression, basically the core arguments presented in the article really were a rejection of OOP information hiding, not really the specific technical implementation of using closures for information hiding.
It does ignore the other benefit of module-closures, though (avoiding namespace collisions). Explicitly exposing your "private" functions (prefixed with _) in the module object would be a better way of achieving what the author wants.