Ideally, that should be all that is needed. However, a large number of judges could easily disagree on NBC status, either from being misinformed, or not willing to rock the boat, or arguing lack of standing (Remember the Supreme Court punted on D'inofrio in 2008).
On the other hand, if Obama is proven not to have been born in Hawaii, that would VERY hard to ignore. As far as I can tell, there is no evidence that Obama was even a citizen. That's why he has the phony SS #s, in my opinion.
D'onofrio didn't have the Minor definition as a legal precedent in 2008. He tried to argue from omission that the 14th amendment didn't define natural-born citizenship. This argument is true, because it was confirmed in U.S. v. Wong Kim Ark, but Leo didn't cite that either. He relied strictly on the construction of the law, and not a citation to legal authority. Second, the appeal had to overcome the lower court's argument that it was filed too late. The SCOTUS didn't have anything to work with.