Nonsense. The "subject to the jurisdiction thereof" deals with the issue of the children of diplomats. They are, AFAIK, the only people born in the US but not subject to the jurisdiction thereof as they are not subject, by treaty, to American law.
Are you arguing that Obama is not subject to the jurisdiction of the US? So, he can commit murder and not be prosecuted for it?
Not just any citizen can be president. If that was true, the founders would have never put the natural born clause in the Constitution.
That's correct- naturalized citizens cannot be President. But any American who was a citizen at birth can.
Also children of indians (subject to tribal law, by treaty), children of hostile occupying forces, and children born on boats, planes, etc. transiting through US waters, airspace, etc. See the link a few comments up.