You are correct. What was cited turned out to be the plaintiff's argument, not the ruling of the court. The court did not address that issue, but instead claimed they had no jurisdiction. (A lot like the "Standing" argument.)
But as I mentioned to Kleon, if Plaintiff's attorney did not think the argument had merit, why would he have presented it to the court? Likewise, why was John Barry's son (of the same marriage and circumstance) permitted to remain with him in England, while the Daughter was not?
Good for you that you were able to recognize it. I looked around and was surprised to see other people using that quote, even after they were shown the truth. One blog went as far to say that it's "the clearest" United States Supreme Court precedent regarding the definition of natural born citizen. Yikes!
But as I mentioned to Kleon, if Plaintiff's attorney did not think the argument had merit, why would he have presented it to the court?
Maybe he believed it to be true, I don't know. We shouldn't assume that anything presented in court must have a kernel of truth to it.
So the case really does nothing to support your position. The opinions of individuals are not the same as judicial rulings. And the court in this case did nothing to clarify the matter.