You can't gloss over the difference between "schema" and "type." Schemas exist at the edges between pieces of software. They govern how you talk to databases or APIs; they needs to be forwards- and backwards-compatible. A type, conversely, exists within one program. You can update types and type invariants without needing to migrate state or make a breaking API change.

"Make invalid states unrepresentable" is much better advice for the internals of a program than it is for the sql or protobuf schemas at that program's margins. The point of "parse, don't validate" is to transform flexibly-represented external data into strongly-typed internal data that respects invariants; since you can update your internal data model much more easily than the models of external data, keeping external data representations flexible is sometimes just as important as keeping internal representations strict.