What the hell...
No. You cannot copyright every single word you ever utter. Sorry. We're not going to be hitting ascorbic's with a class action lawsuit for copyright infringement.
This is quite separate from whether or not it's nice to post private /msgs without permission. Under most circumstances, probably not. However, it is insane to invoke copyright law to defend this.
The cases mentioned above in defense of the copyrightability of private /msgs refer to letters, which are much more substantial works than the 512 character limit on /msgs. In the case of conversation with Hemingway, which is much closer to /msgs than to a possible original creative work like a letter, the copyrightability of conversations was denied. A conversation would need to highlight much originality and convince a judge of being a unique work of authorship which could give the author a monetary advantage if copyrighted. The purpose of copyright is not to enforce confidentiality, but to allow authors to profit from their work which in turn should benefit society by fostering the creation of original works.
Despite the primitiveness of our /msg system, what has been posted in this case is more akin to a conversation than private correspondence. Here is another case in the US, which like Hemingway's, copyrightability of a conversation was denied.
By all means, nuke a writeup that makes a spat public if you so wish. There are reasons to honour a noder's request to not make a conversation public. But please, don't do so invoking copyright law. Copyright law gets abused enough as it is, so don't spread further confusion on the topic.