I had a little trouble registering to vote the first time because the lady didn't realize that Guam was a US territory. lol I had several friends growing up who were born overseas (Germany, Japan and one Commander's daughter who was born in Bahrain) and they are all US citizens. Natural born? I don't know but I would assume so.
Although the constitution does not define “natural born” citizen, my guess is the framers meant any one born as a citizen versus a naturalized citizen.
Any child born of US citizen parents serving military duty overseas is natural born since he/she is citizen at birth.
Obama does not qualify since his mother was not living in US for stipulated number of years as an adult at the time of Zero’s birth, and father was not a US Citizen.