Members can't reset password, since the browser they are using saved some data that makes WA think they are still logged in. This is a very difficult problem to explain to many people and Clearing their Cache is not a thing they do often. Since they can be using any of a number of browsers and versions it makes it hard and time consuming to help them.
Rather than WA reporting an error, I think it would be better to force close anything that is causing this duplicate login problem.

I'm far from an expert here but this is a very difficult problem to troubleshoot with the user. An alternative option would be for the Administrator to be able break any perceived duplicate login session.