Hm, the private tagging was always one of the more reliable features on MG and I can not see a problem now.
When I am searching for the modules name I can not find anything. As expected.
Also nothing leaked to Google.

Be careful: if people visit your public rack with the private module assigned they can see the private module. This is intended and not a bug.
So for now there is not much I can do else than keep an eye on the issue. And to recommend not to upload top secret modules. Sorry.