It was never concretely defined. However, all the legal research done on the topic seems to contradict your interpretation.
The Court would never take your narrow view of the “natural born citizen” especially when there’s no contextual support.
All the legal research of which you've heard. There is plenty of legal research that contradicts the common wisdom.
Here's a little piece for you to look at.
"Except the children of transient aliens"? How did that get in there? (I actually know how it got in there. :) )
Don't take my word for it, look it up yourself.
http://books.google.com/books?id=l3w4AAAAIAAJ&pg=PA51#v=onepage&q&f=false