The author of an anonymous message board post can see and edit their post under the "My Posts" tab. Which means anyone else impersonating them can also either intentionally or accidentally discover the true author.
1) In a malicious setting the impersonator can guess at a range of users who may have made a posting and quickly scan all of the "My Posts" tabs in question.
2) In an accidental setting a user may have requested help and the impersonator happens to come across the anon posts in the "My Posts" tab.
User is truly posting a message that can't be traced back to them
It's still possible to act maliciously to expose the true author and the user may also accidentally expose themselves if requesting support.