As far as the technical part goes, I believe that would be completely doable.
To give a brief outline, a fully private case could be posted directly to the Backroom, and the players involved given a special BM page where they could interact with it—reading messages that were sent specifically to them, and writing messages that would be posted through the server to the Backroom thread.
If you just want to allow people involved with the case to remain anonymous to the playerbase at large, you can take out the Backroom part of that, and just give each player involved a page where they can post to the thread anonymously (though each would be tagged in the case as something like "complainant", "accused 1", etc, so as to know which was which for the case itself).