You just made my day! I had assumed that the Google account was the only dedicated association with my TheOldReader account. That's awesome news!
I've been sitting patiently since July when I set my account up and attempted to convert gReader to TheOldReader and met this problem. Was this feature available as of that time or is it recent? I'm just curious. Also, please make this information clear to the public for others like me that haven't explored the settings and just made an assumption.