The American parent goes to the American Embassy, registers the birth, and the kid is a natural born citizen.
My grandson was born in England. My son went to the American Embassy to register the birth and the kid was a natural born American citizen and issued an American passport right then so he could return to the US whenever his father wanted to bring him here. His citizenship cannot be adjudicated away from him just as his father's can't (or mine). When they came to the US, my son and the baby were in the US citizen line while the mother, being English, was in the foreign line.
You are confused about your grandson. There is no possible way he is a Article 2 Section 1 natural born Citizen. He was registered a code statutory U.S. Citizen via 14th Amendment.