Does TOAST really compress the complete row?

I am confused about one claim in this blog post:
https://www.2ndquadrant.com/en/blog/oracle-to-postgresql-binary-objects

> All columns that come after data > 2000 bytes participate in The
> Large Attribute Strorage Technique (TOAST). This storage is for the
> row, not the column. Your id column comes as the last column in the
> table? Whoopsie, your primary key just got shoved into blob storage
I always was under the impression that TOASTing only happens on column level, not on row level.
The manual does not mention anything about the whole row being TOASTed if one column exceeds the threshold.

Can someone clarify please?

Thomas