When he said, "was born of naturalized parents" is incidental to stress his point beyond doubt; analagous to saying, "my son is an honor student, and he plays varsity football." Playing football has nothing to do with being an honor student.
The very last "citizen of the U.S. by birth" proves parentage has nothing to do with being NBC unless the parents owed allegience to a foreign power. Allegiance comes either by birth or by parentage. Madison says "by birth" is the strongest and "is the policy of the United States."
"All from other lands, who by the terms of [congressional] laws and a compliance with their provisions become naturalized, are adopted citizens of the United States; all other persons born within the Republic, of parents owing allegiance to no other sovereignty, are natural born citizens. Gentleman can find no exception to this statement touching natural-born citizens except what is said in the Constitution relating to Indians. - (Cong. Globe, 37th, 2nd Sess., 1639 (1862))
Parents owing allegiance to no other sovereignth can only apply to ambassadors, etc. Regular people living here or immigrating here transfer that allegiance to the U.S. This is not a hard and fast proclamation that they must be citizens. Many court cases are on record stating that citizen parents are not required to produce a NBC child on American soil.
"Every human being born within the jurisdiction of the United States of parents not owing allegiance to any foreign sovereignty is, in the language of your Constitution itself, a natural born citizen.... - (Cong. Globe, 39th, 1st Sess., 1291 (1866))
In all three instances of Mr. Bingham quotes you provided, he never says citizen parents are required even though it would have been easier.
While there are many cases, this two in particular use the language Mr. Bingham uses and should make sense:
“All persons born in the allegiance of the king are natural-born subjects, and all persons born in the allegiance of the United States are natural-born citizens. Birth and allegiance go together. Such is the rule of the common law, and it is the common law of this country, as well as of England. There are two exceptions, and only two, to the universality of its application. The children of ambassadors are in theory born in the allegiance of the powers the ambassadors represent, and slaves, in legal contemplation, are property, and not persons.” Justice Swayne, United States v. Rhodes, 1 Abbott, US 28 (Cir. Ct. Ky 1866)
“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, and 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. 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.” U.S. v. Wong Kim Ark,169 U.S. 649,658 (1898
I couldn't help but notice that your Article II Facts goes to a birther website. I also notice that they ask for donations. I firmly believe that these people are trying to make money by riling up people who really don't understand the law. They distort and they lie.
I have at least 30 solid authorative references that actually state aliens can produce NBC if they live here.
No birther can produce a document or law that says two citizen parents are required to be NBC unless their child is born on foreign soil. FACT!
If you want, I'll provide my references.