Thanks, seesaw, for that input.
When I post a PM to someone, I see it as kind of like knocking on someone's door and asking, "Mind if I step in for a chat??" If I've decided that I basically don't like you, then why am I coming over to your place? In the context of a thread, which is a group discussion, there's opportunity to post a note saying, "I see things differently from post # 32 above." If I take the discussion to a private message, why don't I want other thread participants to know what I'm saying? Am I sharing a very personal revelation, or do I just not want witnesses to my hostility? I agree that issuing reprimands is not the role of non-moderators.
I think it's valid for contributers to a thread to offer the OP an invitation to "PM me, if you'd like." If, on the other hand, I think the OP is not making sense, then I should just get off the thread.