Thanks for posting the context of those lectures—they say as clearly as anything I’ve seen that natural-born citizen and native citizen mean exactly the same thing. Are you claiming that “natives” means something different than “native citizens”?
See 121. Percy A. Bridgham, aka The Peoples Lawyer explains it far better than I could.
Wouldn't you consider an anchor baby a native born citizen instead of a natural born citizen? Neither parent is a Citizen in any manner yet their child retains jus soli (right of the soil) simply due to their being born on American soil.
What do you call a child born here prematurely while their parents from a foreign country were visiting Disney World on vacation? And what would you call a child born of a foreign Mother going to school here on a student visa that was impregnated by a Citizen Father during a wild fraternity party? If you reverse the roles you've got Obama. (Father student/Mother US Citizen)
Both are here for a single dedicated purpose and neither planned on staying here after their purpose was complete. Either way, some, or all, of their children's parents are foreigners.
None need to be naturalized due to jus soli yet none have complete jus sanguinis (right of blood) (for instance the female visa student could have been impregnated by a naturalized citizen...Indian/ Nat. Indian, Chinese/Nat. Chinese, etc.)
What would you call them besides native born citizens?
They've all become "natives" of the nation in the aspect that we all share place of birth in common. They're extended all rights under law except for the right to run for POTUS.
Now if you take that as me claiming that natives means something different than native citizens then so be it.
I'll leave the legal mumbajumba penumbra up to those who get paid to do that sort of thing.