The problem is that it is not that simple. It depends on what you mean by "public." One thing is to say that the information is "public" because it is widely known to the public; but is a different thing to say that information is "public" because it is contained in a public record that is available to the public.
For this reason, the generally accepted definition of confidential information does not use the adjective "public." According to this definition, confidential information is information related to the representation that is not generally known. (A couple of years ago, the ABA issued an ethics opinion clarifying the notion of generally known information.)
Thus, information can be public (in the sense that it is available to the public) but not generally known, in which case, the fact that the information is public does not change the fact that it is still confidential.
I am writing about this today because a recent decision by the New Jersey Supreme Court, again reiterates that this distinction is important and can result in problems for lawyers, often when the lawyers discuss information about former clients.
The case is called In the Matter of Calpin, and the facts are similar to many other cases that have raised this issues in recent years. A client (or former client at the time) wrote a negative review about the lawyer in Yelp! and the lawyer decided to reply by, among other things, disclosing some information about the client. The information was "public" in the sense that it was available in public records, but is was not generally known and for that reason the court held that the lawyer violated the duty of confidentiality.
To my knowledge, only on case (Hunter v Virginia State Bar, 744 S.E.2d 611 (Va. 2013)) has held that the state can not discipline a lawyer who discloses public information that is not generally known.