Sounds right.
An example, John McCain.
I have always understood that if born of USA citizens anywhere in the world, you are a citizen as much as if you were born in the USA.
Yes, but by operation of a congressionally-passed statute, not by "nature."
Those whose citizenship depends on a statute are not natural born citizens, even though they are (by way of a US law) citizens at birth, no naturalization ceremony. There is a naturalization process however, which involves presenting birth and parent details to the US State Department - typically a US Consulate in the country of birth.
Citizen just as much as born in the USA with the solitary exception that those born out of the US are not constitutionally qualified for the offices of president or vice-president. Well, that would be so if we followed the constitution. We don't, so there is that.