If I may be so bold, I'd posit the misunderstanding is on your part. No one is saying things are impossible to model in rigidly typed systems - this is your key misapprehension about what is being said. What I'm saying is that different languages have different paths of desire, and the kinds of problems identified in the original article are more the kind of problems that tend to crop up with heavy use of types, than they are the kind of problem that has much of anything to do with functional programming.
You're thinking categorically, but I am not, so we're talking at cross-purposes. Perhaps too much static typing has crept into your thinking! (I jest, of course! :) )