A person posting such information would be foolish to say that it is classified. That would only draw attention. Stating it would only serve to satisfy the poster's ego.
In my experience, all people who purport to know secret information (of some variety of "secret") have "authentication narratives", the sole purpose of which is to attract attention AND make people think their information is authentic (because the government generally does not comment on leaks, something external is often needed to prove that they didn't just make the information up). Usually it involves some story about how the FBI showed up on your door or about guys in gray suits taking notes at your exhibit or about copies of your book being confinscated in Washington DC or something like that. I only point that out to note that most people who do this sort of thing WANT attention (whether it is for ego or for political motivation or whatever, varies).
For a government to say that something is classified would bring as much attention as if the user has said so. It would compromise their ability to neither confirm or deny the fact in question, and close their option for plausible deniability.
This is true but in a few instances this has happened, so it is not impossible. Two notable instances are the U.S. v. The Progressive (1979) that I noted earlier, and the Rosenberg trial (1951), which required expert testimony on the exact secrets the Rosenbergs had stolen. Which is how the idea of using implosion for a plutonium bomb entered out of the secret domain and into the public domain.
That being said, non-US governments have done this sort of thing all the time (they are often less worried about saving face). An alternative version of this is that the government of Russia tells us that certain information on Russian missiles is classified and needs to be removed. "Oh, but it was compiled from the public domain!," we/the author says. "Tough luck, that's not how we define secrecy in Russia!" says V. Putin. What would Wikipedia do then? Putin's Russia has actually sent people (Russians) to jail over just this question of what constitutes a secret, as I understand it (a guy named Igor Sutyagin is currently serving 15 years of hard labor for work he did with declassified sources). Would we honor Russia?
FF