Birth notices don’t come from the hospital to the newspapers, they come from the Department of Health (in 1961, it was called the Health Bureau).
The section of the newspapers they were in is called “Health Bureau Statistics.”
The INS memo does name the child:
http://www.wnd.com/files/2012/07/INS-6.jpg
And you do know that births could have been self reported by a parent or grandparent for children not born in a hospital.
What can settle this one about the birth announcements would be if someone saved their hardcopy announcement and the clipping included the people above and below that particular entry.
Would show if 0bamas were listed or if some shenanigans were done with the microfilm.