That is exactly right. If you are an American citizen, that citizenship is in your body - you don't renounce it if you go to another country and if you have a child there, it “inherits” your citizenship and you fill out a form stating such. You are the American (with American reproductive parts) if you are in America or in Pogostan or Magicland or the land of the Wizard of Oz.
“If you are an American citizen, that citizenship is in your body - you don’t renounce it if you go to another country and if you have a child there, it inherits your citizenship and you fill out a form stating such.”
Note that the 9th Circus requires compliance with “residency requirements” for a foreign birth. Only a trial on the merits with full discovery of the birth location, marriage legitimacy of the parents could determine whether the 9th Circus standard #2 is met. The SCOTUS would have to uphold it to extend this definition beyond the 9th Circus (the most overturned Circuit, BTW...thus 9th Circus, IMO).