I'll tell you what a private message should not be, just to shorten this: it is not (or should not be) forwardable. It is not (or should not be) disseminated through blind copies. It does not (or should not) involve more than two people - the original sender and the original recipient.

If you, Matt, send the same PM to five people, then it is not a private message. It is just a message. There's nothing private about it at all.

Likewise...

If I receive a message from Sophie and copy my answer, along with her original message, to her and five others, then it is not a private reply. It's just a reply. And her private message is no longer private, either.

If what I've described above is not how private messaging works - nor how it should work, in most people's opinions- then I want the name of it changed to "on-board email", "the mailing lists", "on-site email" or whatever phrase best connotes no expectation of privacy at all.

I absolutely hate misnomers, especially ones that are as misleading as "private message" is turning out to be - at least judging by this thread.