OK...disregard the diplomatic credentials. Suppose two Chinese exchange students on student visa have a child in the U.S.. They return home when the child is one. At 21, the child returns to the U.S. on a Chinese passport and asserts his U.S. Citizenship based on the 14th Amendment, and obtains a U.S. Passport. 14 years later, is that person eligible to run for president?
I'm guessing you'd argue that he/she is...and I think you'd have a reasonable case; however, I think there are also arguments that could be made against it...
United States vs. Wong Kim Ark decided that very issue. The child is a citizen, but not a natural born citizen. The decision states that very clearly.
The Constitution and the applicable Supreme Court decisions would seem to indicate that they are. But let's take a more likely scenario. Two foreign nationals move to the U.S. legally and have a child. That child is born in the U.S., raised and educated in the U.S., attends university in the U.S., never spends one minute living in the land of his birth parents but instead spends his entire adult life in the U.S. Why should that person's loyalty be questioned and he be denied the chance to run for president? What clause in the Constitution or U.S. law or Supreme Court decision supports their inability to be president?