Regarding Vattel, you are correct.
But, under the Naturalization Act of 1795, he was ineligible. The State Department manual states that individuals born overseas to parents in the military may not meet the Constitutional definition of natural born citizen.
Additionally, to my knowledge, no one has claimed that the United States recognizes anyone other than citizens born overseas to diplomats in service to the nation as anything other than citizens, which is right in line with the various Naturalization Acts going back to 1795. Military bases are not sovereign territory; there are court cases providing precedent to support this.
So, there are a number of problems with making the assumption that you've made. Yes, it sounds unfair, but the law is the reality and it is what it is. McCain's eligibility was on shaky ground, just as shaky as Obama's. But, McCains's got a great deal of play in the media and a very questionable Senate Resolution. Obama's got swept under the rug.
The statement about US bases abroad not being US territory is true, but most often comes up when one parent, usually but lately not always, the mother, is not a US citizen or national.
One female solider I know of, she was the singer in a coworker's band, is married to a German national. (He was appalled when she was handed an AR-15 after one practice session, went prone and drilled the target. :) )
It also has come up when neither parent is a citizen, but a birth still occurs on a US base.
I've read that state department manual, more than once. It was written after children born abroad to citizen parents were once again made citizens at birth by statute. The state department is not concerned with natural born citizenship, as they admit, just citizenship. Those cases which would fit "natural born" under the Vattel definitions, would be citizens anyway, so they don't devote much verbiage to that, beyond indicating the documentation requirements.
That manual also says such children of two parents born abroad, or anyone else born abroad but a citizen at birth is natrual-born, under the statutes. If the statutes are wrong on that, they can also be wrong the other direction, and they are.