The Directions web app template calls the premium service https://route.arcgis.com, even when subscriber content is unselected in the web app's configuration.
This behavior is expected. The checkbox for the routing service is to create a proxy to it so that the app can be shared publicly and the end user is not prompted for sign in. Keeping the box checked OFF means you are not creating a proxy to the service, and therefore, the end user will be prompted to log in with their credentials in order to authenticate access to the routing service.