Yet you can be granted citizenship by other nations, and it will be accepted. So is the problem with dual citizenship or not?
NBC is a condition of birth which is impervious to foreign claims. If a person, after the age of majority undertakes to acquire and is granted citizenship of another country, that has nothing to do with and does not negate NBC status.
“The problem” with Obama is that his stated biography (assuming a non-bigamous marriage of his parents) with his UK subject father would make Barry “governed by the BNA of 1948” and thus a dual UK-US citizen at birth. Barry would be a native born citizen (born on US soil if, indeed, he was) but not a natural born citizen, according to some constitutional scholars.
If Barry's parents had a bigamous marriage due to his father's previous Kenya marriage to Kezia, Barry would be the illegitimate son of a legally single US citizen mom and would be NBC under US law because he would not be a dual citizen. The BNA of 1948 does not pass citizenship to illegitimate children.
If Barry were actually born in Kenya and his HI vital record came about as a result of a fraudulent report of a home birth or some sort of post-birth amendment (so far hidden by HI vital records due to Barry refusing a release) Barry would not be NBC or even a US citizen due to the age of his mother under US law at the time.