Earlier quoted context omitted.
I don't think this literally means each user of your app gets their own DB user, rather that you create different db users for different aspects of your app. What you're describing is what RLS (row-level security) is for, where you log into a generic global "app_user" user with certain permissions that don't include things like admin tables etc, and then define the specific user that is using the session via session…
There are applications that are built to where literally every user gets a database login. For example Dynamics SL (formerly Solomon) is built this way with MS SQL server.
The SaaS build of the app even exposes this in the URLs. Everyone is on the same codebase, and there’s just some additional database logic to connect the right deployments to the right databases.