The point of the article is about locality of validation logic in a system. Parsing in this context can be thought as consolidating the logic that makes all structure and validity determination about incoming data into one place in the program.
This lets you then rely on the fact that you have valid data in a known structure in all other parts of the program, which don't have to be crufted up with validation logic when used.
Related, it's worth looking at tools that further improve structure/validity locality like protovalidate for protobuf, or Schematron for XML, which allow you to outsource the entire validity checking to library code for existing serialization formats.