Your statement about race is true. In 1961 white or black or negro or colored would have been on there for race.
The other thing is that a certified copy is certified by someone who made the copy in the office of vital records. The original was signed by someone and that signature remains a part of the permanent record. Then the copy is certified by the clerk making the certified copy.
Obama would not have changed the race to African since he would love to maximize the impact of having his father called a Negro or colored to emphasize it and once again play the race card.
In 1961 you could get almost anything since it was up to the local authorities to decide what race you were, and what a race actually was.
The federal government had not yet imposed their nonsense system on everyone.