It's not that you can't have a secret and be on Facebook-- it's that you can't have anybody who knows your secret be on Facebook.
Put another way: even if "Joe" (from the article) were not on Facebook, that wouldn't have stopped someone from posting a comment about his boyfriend.
People talk about other people. You can't control what they say. If these people are publishing their comments (to their "friends", or on blogs, to the general public), you're shit out of luck.