I thought a baby born overseas to 2 US citizen parents was automatically a "natural born" US citizen -- but there might be extra paperwork involved unless they were born in a US embassy or perhaps on a military base.
I have a doctor friends who was born in the US embassy in Cameroon (might not have been called that at the time.) His parents were missionaries. He travels to Africa occasionally, but he avoids Cameroon because he doesn't want to get conscripted (kidnapped) into their military. I don't know if that's a real risk or an imaginary one. In college, he tried to join some kind of African-American group just to cause trouble, and they didn't see the humor in it. He was more African than probably any of them even tho' he's white :) I bet they would really get upset with a white applicant from South Africa.
This is true, and yes there is one extra sheet of paper. American parents that have a child overseas must obtain a Consular "Report of Birth Abroad". This grant the kid birthright citizenship and serves as a de facto Birth Certificate, since the actual certificate is often in a foreign language. I routinely offer my Birth Certificate when asked for it and watch folks try and read the Italian, before giving them the ROBA.
This process has not changed.
As Ben pointed out the article is so obscurely worded as to cross the line into lying. The policy change only applies to a *very* small set of cases of a foreign born child (born to foreign parents) that is adopted by US citizens, in a foreign country. They would then have to apply for naturalization papers for that child, which, in that category, is pretty much automatically granted. ICE changed their policy to conform to the Dep. of State's policies because the differences in the two was causing confusion.
This (as you might expect) blew up on US Military social media pages and took about 15 minutes to run down the truth and spread it on the same pages. I guess the media couldn't be bothered to read the policy.