Originally Posted by
LupineChemist
Can you expand on this? What sort of hassles?
Airline reps or contractors might see the US place of birth and insist that you have a US passport or badger you on why you don't for the trip.
CBP has made stinks about such situations too -- anything from "you still need a US passport" rants to "why would you give up this up" suspicions/paranoia that result in secondary examinations that eat up a lot of time.
Originally Posted by LupineChemist
Just out of curiosity, are there any other cases other than children of diplomats where someone born in the US is not a citizen?
Other than diplomats, the only other category would be if a child were born in the US to a parent representing a foreign military powers of some sort in a hostile action in US territory over which the U.S. had no control at the time of the birth. Can't recall a single such US instance for a non-diplomat's child, at least not in my lifetime or that of anyone I've known to work at State since the UN came into being.
Probably not looking for this, but we still have US-born nationals who are not US citizens; now mostly -- if not, by now, just exclusively -- those of American Samoan heritage. For them we have US passports that are for non-citizen US nationals. This can be tricky sometimes as in if the non-citizen US national applies for participation in a program that requires US citizenship rather than merely US nationality. [US citizenship is, quite obviously, a very large subset of US nationality.]