That doesn't make logical sense, and even if it did, it omits obtaining certification via U.S. Citizenship and Immigration Services, which is not the same as diplomatic recognition.
The statute says what it says, "shall be nationals and citizens of the United States at birth", and the USCIS webpage says,
Form N-600, Application for Certificate of Citizenship, is filed to obtain a Certificate of Citizenship which serves as evidence of your or your child's U.S. citizenship. You may file Form N-600 if you were born abroad and are claiming U.S. citizenship at birth through your parents. You may also file Form N-600 to obtain evidence of citizenship if you automatically became a U.S. citizen by operation of law after your birth but before you turned 18 years of age.USCIS FAQ Page
If you and kabar are correct, that paragraph would read remarkably differently. Perhaps along the lines of:
Form N-600, Application for Citizenship, is filed to obtain a Certificate of Citizenship which creates your or your child's U.S. citizenship. You may file Form N-600 if you were born abroad and are seeking U.S. citizenship at birth through your parents.
Under your and kabar's view, the USCIS sentence about citizenship being automatic for some foreign born persons is impossible. No foreign born person automatically becomes a US citizen by operation of law.
Perhaps you did not understand the terminology. A person can possesses a right to possess a tangible or an intangible asset, but that person may then fail to possess that asset by failure to actually secure it and take actual possession of the asset before the asset is lost to the person having the right to possess the asset. The same is true of citizenship in some cases. It is not enough to be born with the right to possess citizenship. A person must act to secure the citizenship and defend its possession. While a natural law can authorize the right, recognition, and exercise of natural born citizenship and an unnatural and artificial statutory law can authorize the right, recognition, and exercise of native and naturalized citizenship; a person must still act to secure the citizenship and defend it against those persons and organizations who would otherwise deny the right of citizenship. Example: even though a person is a natural born citizen, born in the United States with U.S. citizen parents, the Real I.D. law can allow the TSA and the U.S. INS to deny recognition of the U.S. citizenship of persons identifying themselves with a driver’s license identification card from the States of Illinois, Missouri, Texas, Wshington, and perhaps other states. In other words, whether or not you are a person who has a right to claim citizenship at birth or after birth, your right can be denied by the government under certain circumstances, unless you successfully defend the right with other forms of identification acceptable to the government. Consular officers are diplomatic personnel from the Department of State. They have the authority to deny recognition of U.S. citizenship whether or not it was actually a right at birth.