Original sin is not a genetic disorder. I think that Paul was correct, that through Adam sin entered the world (original sin) and through sin death, and death spread to all man for all have sinned and fallen short of the glory of God. Jesus did not sin, yet He set aside His own glory - not counting equality with God a thing to be grasped He humbled Himself by becoming obedient even to death.
We are human by birth, born under a curse, born "in Adam", born with desires of the flesh that are not always "in tuned" with God's will (e.g., when Christ prayed "not My will but Thine be done"). But "sin" does not occur until act on our desires above God's will (e.g., sin happens when we are carried away by our own desires).