I dont think the issue is so much "anonymous" posting as much as it is about keeping dirty laundry inside and not airing it to the unwashed masses...
I appreciate the rationale for the proposal, but the devil is in the details.
And most importantly.. any expectation of privacy.. in an internet forum.. is inversely related to the number of people who have access to the forum. Once you have more than a dozen or so peeps, there really ISN'T any enforceable sense of privacy to one's statements.
My feelings are that any "semi private" or "private" forum will be duplicative.. and provide privacy in name only... and would be an exercise in futility and false security.