Those who suggest that there is no distinction between "citizen" and "Natural Born Citizen" would have us believe and accept that such a person might have been eligible to run for President of the US simply because he was born in America. According to defenders of the alleged eligibility of Barack Obama (or Marco Rubio, or Bobby Jindal), any person born on US soil to one or more alien citizens could be the leader of the free world. At some point, according to that path of logic, this should have included Anwar al-Awlaki.
So, to say that every child born in America is a natural born citizen is also to say that any foreign interest whose child was born in the US could be allowed to raise that child abroad as an enemy of the US and return that child to this country in time to meet the Constitution's 14-year residency requirement for President.
Considering that Islam has been at war with itself and the rest of the world at least since the death of Muhammad almost 1400 years ago, it takes very little imagination to project how a powerful enemy of the US might take the necessary 35 years and other resources to groom a "Manchurian Candidate" for the US Presidency. If we accept the premise that every person born in the US is a natural born citizen, we allow the establishment of a flawed precedent permitting a family such as that of Anwar al-Awlaki (or a communist government, or a Mexican drug cartel, etc.) to gain control of our country through an orchestrated, long-term attack on the Presidency.