I have grown up in an English speaking household, literally brought up on american culture and TV/movies, yet my English is totally neutral in accent.
We have an american school in Pakistan too, I have yet to meet people who speak american accent english after studying there since childhood under US teachers influence, they my say erb instead of herb but thats it.
Yes those who do speak in UK/US style are born or raised there, but no 18 yearold going for studies abroad will come back with an accent, or start speaking it by watching TV/movies, extremely rare are some older people who will speak with a faux accent made up by themselves from British English, how you people do it is interesting, and its not like your ancestors spoke american accented english en masse, it was more mediterranen style.