External users means the username, password, and all user data is stored in a separate DB, for example, in WordPress, and Q2A uses those users. I don't think you're using that. If you're using LinkedIn to register/login then you must have downloaded the q2a-open-login plugin. Maybe the issue is in there.
Regarding the backup, I wouldn't remove that as possible reason either but seems to be less likely now.
Regarding the upgrade to 1.8 I don't think it will solve the issue. The closest thing to your issue is that there have been changes in how passwords are stored. I don't think that has anything to do with this anyway.
Without having step by step instructions on how to reproduce it locally there isn't much I can do. I mean, I have logged in many times with the same and different users in the same and different browsers and never faced that. However, I never used the q2a-open-login plugin. If more people report this and happens to be using it then it is a good place to start. I'd pay more attention to what provider (LinkedIn, Facebook, etc) are using the users that face this issue, or maybe if the same user is using more than one provider, and what providers are using the users that get somehow mixed. Just trying to find some pattern there.