This is a great article, but people often trip over the title and draw unusual conclusions.
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.
I disagree. I think the key insight is to carry the proof with you in the structure of the type you 'parse' into.
I think that's an excellent way to build a defensive parsing system but... I still want to build that and then put a validator in front of it to run a lot of the common checks and make sure we can populate easy to understand (and voluminus) errors to the user/service/whatever. There is very little as miserable as loading a 20k CSV file into a system and receiving "Invalid value for name on line 3" knowing that there are likely a plethora of other issues that you'll need to discover one by one.
When I came to this idea on my own, I called it "translation at the edge." But for me it was more that just centralizing data validation, it also was about giving you access to all the tools your programming language has for manipulating data.
My main example was working with a co-worker whose application used a number of timestamps. They were passing them around as strings and parsing and doing math with them at the point of usage. But, by parsing the inputs into the language's timestamp representation, their internal interfaces were much cleaner and their purpose was much more obvious since that math could be exposed at the invocation and not the function logic, and thus necessarily, through complex function names.