As I understand this, the quotes are from an 1845 chancery court in the State of New York? I much prefer SCOTUS precedent on this issue.
The WKA decision used the same reasoning as the 1844 decision, arguing that WKA met the criteria for a natural born citizen and was thus a citizen of the USA per the Constitution.
I think WKA was a less well documented decision than the 1844 case.
WKA: http://www.law.cornell.edu/supct/html/historics/USSC_CR_0169_0649_ZO.html