That is exactly what my BC looked like. I was born at home and never had a BC until I was ready to apply for SS. I sent to my state of birth to get one and when it came it was a CARD partly filled in by my mother, then other parts were typed. One place that was typed was my name as evidently she didn't know what to name me at the time. There was a doctors signature. This was then COPIED onto THE SAME GREEN LOOKING type of security paper as the forgery of Obama's. It then had the State Seal impressed in it. Since my mother had passed by the time I got my BC it made me tear up to see her hand writing on my BC.
So IMO IF Obama had been born at home and his BC looked like that it would be no big deal.
If Obama had been born in the home of that family with whom the grandparents were living at the time, you can be damn sure that the family living there would have remembered it. The daughter of that family has already said she doesn't remember any baby there.