In the first case, the invited external person hadn’t clicked on the link in the invitation email and associated their identity with the invitation token but then tried to follow links to content areas on the site and sign in with their Organisation account. Regardless of the invited email address and the login email address matching, the token from the link wasn’t setup.
In the other case, through an initial confusion, the person signed in with their Microsoft account rather than their Organisational account and later tried to sign in with their Org account.
If that doesn’t help, contact your support team and include these technical details:
Correlation ID: <Unique Correlation ID>
Date and Time: 29/09/2014 01:42:58
URL: <Your SharePoint Site >
Issue Type: Partner User Invalid.
Either re-invite or advise the person to click on the link in the invitation email.
Delete the user from the site that you invited them and re-invite them. If you don’t you’ll end up with two similar accounts and it could be difficult to tell them apart.