qwertyisback
you are correct....
I have a distant cousin who was born in the US, his father was a diplomat and they applied for Indian citizenship for the child. Two years after he was born they went to Africa for a few years and then to India. When he was 19, he took his birth certificate to US Consulate in India and got his US Passport and came to USA to study. No Oath ceremony, nothing.
He never stopped being US Citizen even though he had Indian Passport.
Parents can choose to give up US citizenship of the child as far as foriegn governments are concerned, but as far as US Govt. is concerned it does not make any difference what the parents choose. The kid will be a US citizen unless he/she chooses to give it up after 18.