“I think the intention is as you state it - never any division of loyalty, on any basis, from the day you are born until the day you take the office.”
We know it is so, based upon the history of the common law that originated naturalization of commoners in the Naturalization Act of 1541 for England. The shifting means of determining citizenship on the basis of jus sanguine and/or jus soli and related doctrines all arise out of the need to determine who owed an obligation of allegiance and obedience to the sovereign in exchange for protection from the sovereign. The conflicts in allegiance is what compelled a move away from feudalism towards nationalism and nationality as a form of citizenship. Blood relationship and place of birth are only means for determining a more reliable means of determining and enforcing allegiance.
It pretty much has to be as you say. Otherwise a person born NBC is forever eligible, even if they renounce US citizenship.