The grandmother would have had to say that the baby was born at home, maybe this explains the phony address in the paper.
From other items I’ve read, the people living at that address in the newspaper birth notice were not related in any way to BHO II.
As for the newspaper birth notice..... My daughter was born in TX. Her maternal grandfather here had NINE brothers and sisters in Racine WI. This was his only grandchild and he was the oldest of all of his sibs.
He could easily have notified the local newspaper in Racine to post the birth notice for his siblings, so they would know they now had a niece. ......That was in 1964, so there was not anything like email for rapid communication.
My point is that a newspaper birth notice is meaningless. And, it certainly has no bearing on a person being a “natural born citizen” of the USA.