The article describes a way to use one database for all users, and mentions cases like "each user can see all posts, but can only see the author field on posts

The article describes a way to use one database for all users, and mentions cases like "each user can see all posts, but can only see the author field on posts they made". The difference between that and a database-per-user design is that in a database-per-user design, there's no shared data (or if there is, it's manually synced in to all of the databases by something outside of the database).