The problem with your position is that unless Haley’s parents registered her birth with the Indian government, she was never an Indian citizen and thus, born in the United States and not subject to any foreign power. India does not automatically confer citizenship upon the children of their citizens that are born abroad unless they are diplomats.
American Indians are not a good analogy, as they were considered separate sovereigns and not subject to the law of the USA within the confines of their reservations. So until that law was passed, any child born on a reservation was considered to have been born in a foreign country.
As is any child born here to parents subject to the jurisdiction of a foreign government.