My wife was adopted in the 1960’s in Virginia. She was born in Ohio, and the BC in Ohio was changed to reflect the adopted parents name; date, time, location, doctor all remain the same. There is no notion of “amended” or anything on the BC to indicate that she was adopted or that there ever was a prior “original” BC in existence. The only way she knows different is that her adopted parents told her, and provided a copy of the adoption papers which indicated who the birth parents were.
This chart omits one other consideration-that of a child born to to US citzens abroad while serving under military or governemntal directive. Such children are still, as I understand it, Natural born. John McCain falls in to this circumstance, as does my son. My Son was issued a “certificate of birth abroad of a US citzen” by the US Embassy in West Germany. He is a natural born citizen.
McCain was born under similar circumstances in the Canal Zone, which was incidental to duty abroad of his father.