US vs Ark not only grants citizenship to those born under the jurisdiction of the USA; the decision specifically says “natural born subject”.
Yes. That's right. Obama's father was not some diplomat with immunity. While in the US, Obama Sr. would have been "under the jurisdiction thereof", just like Ark's parents were.
You are forcing the assumpotion though that a Supreme Court case deals with generalities when it does not.
The Court in the US vs Ark Case was not dealing with the eligibility for president clause of the Constitution but only with citizenship.
Eligibility for president is something completely different than citizenship.
Court cases deal with specifics and not generalities.