The sentence you quoted does not occur in the article, so I'm not sure about the context. But generally speaking, the problem is that an app might accidentally do:

  db.exec("INSERT INTO values (t) VALUES (?)", now())

and now your timezoneless column t probably contains the local time.

A lot of code (including ORMs) assumes local time zones everywhere. It's simply hard to avoid, and too easy to accidentally insert bad data.

But the above bug does not happen if your column is declared as something like "TIMESTAMP WITH TIME ZONE" (PostgreSQL, BigQuery, etc., or just "TIMESTAMP" in MySQL).