It's not a privacy implication, it's an anonymity one. Different things. If you want privacy, use PGP or check the appropriate setting in Facebook to make sure

It's not a privacy implication, it's an anonymity one. Different things. If you want privacy, use PGP or check the appropriate setting in Facebook to make sure only the intended recipient(s) sees your message. If you want anonymity for publicly broadcast messages of anything you say, that's a lot harder since one can infer on content as well as style and draw inferences around collections of lies just as easily as collections of truths.