Wrong. You are quoting one isolated paragraph that DOESN'T decide one way or the other, and ignoring the rest of the decison which does decide.
"It thus clearly appears that, by the law of England for the last three centuries, beginning before the settlement of this country and continuing to the present day, aliens, while residing in the dominions possessed by the Crown of England, were within the allegiance, the obedience, the faith or loyalty, the protection, the power, the jurisdiction of the English Sovereign, and therefore every child born in England of alien parents was a natural-born subject unless the child of an ambassador or other diplomatic agent of a foreign State or of an alien enemy in hostile occupation of the place where the child was born.""III. The same rule was in force in all the English Colonies upon this continent down to the time of the Declaration of Independence, and in the United States afterwards, and continued to prevail under the Constitution as originally established."
More paragraphs:
There are some exceptions which are founded upon peculiar reasons, and which, indeed, illustrate and confirm the general doctrine. Thus, a person who is born on the ocean is a subject of the prince to whom his parents then owe allegiance; for he is still deemed under the protection of his sovereign, and born in a place where he has dominion in common with all other sovereigns. So the children of an ambassador are held to be [p660] subjects of the prince whom he represents, although born under the actual protection and in the dominions of a foreign prince.
3 Pet. 155. “The children of enemies, born in a place within the dominions of another sovereign, then occupied by them by conquest, are still aliens.” 3 Pet. 156.
and on and on.