"The Constitution does not, in words, say who shall be natural-born citizens. Resort must be had elsewhere to ascertain that. At common-law, with the nomenclature of which the framers of the Constitution were familiar, it was never doubted that all children born in a country of parents who were its citizens became themselves, upon their birth, citizens also. These were natives, or natural-born citizens, as distinguished from aliens or foreigners. Some authorities go further and include as citizens children born within the jurisdiction without reference to the citizenship of their [p168] parents. As to this class there have been doubts, but never as to the first. For the purposes of this case it is not necessary to solve these doubts. It is sufficient for everything we have now to consider that all children born of citizen parents within the jurisdiction are themselves citizens."
http://www.law.cornell.edu/supct/html/historics/USSC_CR_0088_0162_ZO.html
Since the issue wasn't addressed there, it was covered by WKA in the 1890s.
What you underlined says nothing about natural born citizenship, but instead is referring to a second CLASS of citizen, of which there is doubt about their citizenship. When Waite says there's no need to solve these doubts, he's doing so because Virignia Minor fits the FIRST class of citizen ... NATURAL BORN CITIZEN. The Wong Kim Ark decision AFFIRMED Waite's definition and only dealt with the second class of citizenship for Ark.