I would assume ‘natural born’ to be considered a necessary (for purposes of establishing a standard) but not in itself sufficient basis for establishing such an allegiance—but it is of course the one in the Constitution.
[Though we all know immigrants with as great or greater an allegiance to this country as many native (natural born) citizens.]
We are each and all born into a world with natural loyalties — at birth — to parents and to place. Those loyalties can be at odds. “Natural Born” means those circumstances of birth where the born allegiance is not at odds. For example a child of American’s on temporary travel abroad would have no natural allegiance to France, or Kenya — his or her allegiance would be to the permanent residence of his parents and where the child grows up.