The entire concept, as I see it, is to move any discussion away from this format, to one that the MSC staff control.
My concern would not be as much about friends knowing that I MS, but the clients I evaluate knowing that. And it seems that anyone who became a member of said private group would then have access to who all the members are...so not really that private.
Back when I worked for an MSC, I would take meetings with clients who would often ask, "How can we improve our scores?" My answer was usually, "Stop spending time & energy trying to figure out who the shopper is, and simply treat every customer like they are a mystery shopper."
The MSCs can apply the same logic to their operations. If they want to avoid complaints and criticism, simply operate their business in a way that is beyond reproach.