I was looking at my test site and found that the thought is in your personal text in your Forum Profile, and can be cleared from that screen. It seems that the Personal Text box is set from a Thought when the thinker clicks 'Posterity' from the Action menu of the thought itself. Sorry if that is unclear! But it seems that once you have clicked Posterity then the thought is in your Personal Text and viewable by all, whether the thought was private or not.
I have not tested this on Wedge as I have never posted a thought (I'm evidently not very deep :) ).