Ummm, the "minority" didn't object that the ruling would make Wong Kim Ark eligible to run for president. The dissent agreed with the majority that NBCs are those persons born in the country to parents who were its citizens. It also agreed that persons born in the country to resident aliens could be citizens, but not Ark, because it was specifically forbidden by a treaty with China of which his parents were subjects. Here's where the dissent shows how it agrees on defining the latter class of citizenship:
is it not the proper construction that all persons born in the United States of parents permanently residing here and susceptible of becoming citizens, and not prevented therefrom by treaty or statute, are citizens
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the Fourteenth Amendment does not exclude from citizenship by birth children born in the United States of parents permanently located therein, and who might themselves become citizens
"I submit that it is unreasonable to conclude that “natural-born citizen” applied to everybody born within the geographical tract known as the United States, irrespective of circumstances, and that the children of foreigners, happening to be born to them while passing through the country, whether of royal parentage or not, or whether of the Mongolian, Malay or other race, were eligible to the Presidency, while children of our citizens, born abroad, were not."