Different positions, lots of noise from various attorneys, activists, even the USC to back it up.
But at the Department of State website, we have an interesting document:7 FAM 1100 ACQUISITION AND RETENTION OF U.S.CITIZENSHIP AND NATIONALITY
This is the Consular Bible. All the usual situations are discussed. However, "Natural Born Citizen", which is the term of interest for presidential qualification, is not discussed. It isn't since they don't care: they are just trying to establish who and how you become a citizen.
And what I find most interesting is this:
"Pursuant to this ruling:
(a) Acquisition of U.S. citizenship generally is not affected by the fact that the parents may be in the United States temporarily or illegally; and that
(b) A child born in an immigration detention center physically located in the United States is considered to have been born in the United States and be subject to its jurisdiction. This is so even if the child’s parents have not been legally admitted to the United States and , for immigration purposes, may be viewed as not being in the United States
Itchy trigger finger. Hit Post too soon.
Meant to add: So the State Department on its own now declares that the Children of Illegal Aliens are citizens.
There is not now nor has there ever been a court case that established this. The famous case in U.S. v. Wong Kim Ark only established the citizenship of children of aliens LEGALLY in residence.
But the DoS just made up their minds and said this is what it is. Not the Congress; not the populace; not even the Judiciary.
Some bureaucrats.
Which is also what happened with Soetoro. They just make it up to suit the political winds.