Except, I guess, in that it can be pseudonymous. It's possible somebody knows who I am in real life, but it's also possible they don't (given the way I always connect). You may or may not count that under your definition of "private".
That's not security through obscurity. That would be if I reversed all my posts front-to-back without telling you, or something. Anonymity and pseudonymity are totally legit things with a long and continuing history.