The way I've thought about it, though, is that it's possible to design a program well either by encoding your important invariants in your types or in your functions (especially simple functions). In dynamically typed languages like Clojure, my experience is that there's a set of design practices that have a lot of the same effects as "Parse, Don't Validate" without statically enforced types. And, ultimately, it's a question of mindset which style you prefer.
The real world often changes though, and more often than not the code has to adapt, regardless of how elegant are systems are designed.
Start with a more dynamic type, do stuff that doesn't care about the shape, parse into a more precise type, do stuff that relies on the additional invariants, drop back into the more dynamic type again.