I figured out the answer, it can be found here: Authentication | Twitch Developers under the heading “Refresh in Response to Server Rejection for Bad Authentication”. I’ll just quote:
On seeing a 401 error with a WWW-Authenticate header, an application should try to refresh the session if a refresh token is present. If the refresh fails, the application should re-prompt the end user with another authentication dialog via the standard OAuth 2 flow.
So, they should be treated as equivalent cases.