Making up what you want Ark to say doesn't mean it says that. What Ark does say is:
The real object of the Fourteenth Amendment of the Constitution,in qualifying the words, "All persons born in the United States" by the addition "and subject to the jurisdiction thereof," would appear to have been to exclude, by the fewest and fittest words(besides children of members of the Indian tribes, standing in apeculiar relation to the National Government, unknown to the commonlaw), the two classes of cases -- children born of alien enemies in hostile occupation and children of diplomatic representatives of a foreign State -- both of which, as has already been shown, by the law of England and by our own law from the time of the first settlement of the English colonies in America, had been recognized exceptions to the fundamental rule of citizenship by birth within the country.
Then Ark goes on to cite Cranch where Justice Marshall laid out that all foreign persons in the country that are not foreign ministers are subject to the jurisdiction of the country they are in and no government would willingly give up that jurisdiction.
Ark then goes on to say the following about subject to the jurisdiction as used in laws and cited by courts and how it can be presumed for the legislators and courts to understand it:
This presumption is confirmed by the use of the word "jurisdiction" in the last clause of the same section of the Fourteenth Amendment, which forbids any State to "deny to any person within its jurisdiction the equal protection of the laws."It is impossible to construe the words "subject to the jurisdiction thereof" in the opening sentence, as less comprehensive than the words "within its jurisdiction" in the concluding sentence of the same section; or to hold that persons "within the jurisdiction" of one of the States of the Union are not "subject to the jurisdiction of the United States."
No. Elk doesn't prove that at all. Ark would actually prove that to be false since in Ark, the parents being Chinese, had allegiance to China and could not ever become US citizens themselves under the Chinese Exclusion Act.
Elk cites several cases where Indians were released because US courts did not have jurisdiction over tribal members. Once again, this is about jurisdiction. Elk lays out how Indian tribes as a separate entity in the US are outside US jurisdiction.