The Preamble to the Constitution, which stated the Framers' intent, says that the Constitution was "ordained and established... to secure the Blessings of Liberty... to ourselves and our Posterity."
"Ourselves" means "We the People," the citizens of the United States who established the Constitution and delegated our powers to the states and the federal government.
"Our Posterity" means the children born to We the People, the citizens of the United States.
The "Blessings of Liberty" means that only the Posterity of We the People can ensure Liberty by being allowed to hold the highest office in the land. No other office in the Constitution has this requirement, meaning that the offices of representation are open to all citizens, but the executive office is limited to the Posterity of We the People.
Resident aliens are not "We the People," as they are not citizens and cannot vote for Representation in the House. Therefore, the children of resident aliens are not the "Posterity" of "We the People."
Since resident aliens are expected to be here for a long time, it is reasonable to assume that they will have children. Their children may be born here, but they are not citizens descended via parentage, as their parents are still citizens of their home countries. They are not the Posterity of We the People.
It gets even murkier when the parents aren't even resident aliens, but people on temporary visas, such as tourists, students, and specialty or seasonal workers (L1, H-1B, H-2B). These people had no legal expectation to remain here, so their children born here should have no legal expectation of being natural born citizens here. They are not the Posterity of We the People, but the offspring of passers-by.
-PJ
Natural Born is President specific...you can't just stick it in where you please.