If someone doesn't want it public, the admins can move a thread to the coffee shop. Often they use their judgment to do that when posts of a personal nature are made even if it isn't requested by the original poster. I'm sure if there is something in particular you or someone else has in mind, it can be looked at and possibly moved no matter how old it is.
As you know, in general, no one should assume that any internet communication is absolutely private no matter what the rules of a particular forum or site are. To be sure, it is more private to have a forum that can't be reached by normal searches on Google or Facebook. But there's nothing stopping members of a forum from copying and disseminating the posts. And there's often nothing stopping forum owners from changing private forums into public ones at some point in the future.