Dr. Doogie said:
The announcement appeared on February 11th, eight days after the supposed birthday of C. The announcement mentioned that Mr. & Mrs. _____ had a baby girl. The paper is for the city that C believes that she was born in.
You are correct in that this announcement is the major stumbling block in our search. One possible scenario (however unlikely) is that the "parents" did in fact have a girl born on that date, but that child died. They then may have replaced that child with Anna, giving her the dead girl's identity. (This possibility is often referred to here on WS as a "Delia Cly" situation because there was a woman here for awhile claiming that exact scenario - it later turned out that she was not mentally stable and was a hoax, but the scenario is a plausible one.) There may be other scenarios that would explain how C has a birth announcement but could still be Anna, but I am not aware of them.
The one big thing that tells me that something is fishy about C's birth is the lack of a birth certificate. The only BC that she has is one issued recently by her state with the minimal information that she "knows" about her birth. I know that in California, a BC is required to enroll in school and to receive a first driver's license. How she survived into her late thirties without a BC is a mystery.