From what I recall copyright applies to any original composed media at the point of its creation. There are fair use exemptions in the US for things like critique and parody but not for replication and redistribution. That all said, I would think logically that the public posting of a private message would potentially fall under a violation if someone really pushed it, but it gets fuzzy. A public statement no longer has any reasonable expectation that it be constrained to any particular person so I think at that point the horse left the stable.

An area that I find interesting in a legally dubious sense is the space of revenge porn sites. If the person posting it was also the one filming it, with consent at the time I would think that technically they own the rights to it to do as they will, but that's not the case according to plenty of places with laws against it.

Not a lawyer by any means, but I tend to make them nuts when talking to them just with all the 'what if' corner scenarios my mind cooks up.