Login flow is not consistently started from Reauthentication entry point

Steps to reproduce the behavior

1. Log into the app with a WP.com account
2. Disconnect the app from the WP.com account using https://wordpress.com/me/security/connected-applications
3. Go the the posts screen and back to the home screen
4. Observe a pop-up saying “Connection error: Incorrect username or password” with “Cancel” and “Settings” buttons.
5. Tap “Settings” and get taken to the settings screen for the blog.
6. At this point, I basically seem to be in a broken state. There’s not an account to log out of and I can’t log in with a WP.com account. At the same time I am sort of logged in because it still shows that I have the account’s sites, I just can’t do anything with them.

Expected behavior

I was expecting a Reauthentication pop-up that would take me back to the login flow.

Note: these steps were originally provided by @mchowning in pbMoDN-ET-p2#comment-1203

Start by reproducing the listed account-disconnection steps and trace the action taken when the error dialog's “Settings” button is tapped. Compare that path with the expected Reauthentication flow; done means the disconnected account returns the user to login instead of leaving the app in a broken state.