Why didn't Osama Bin Laden know that?
He expressed concern about it in a letter to Al Qaeda leaders in 2010 during the trial of Faysal Shahzad, the guy who completely screwed up his mission to detonate a car bomb in New York City in 2010.
"Perhaps you monitored the trial of brother Faysal Shahzad. In it he was asked about the oath that he took when he got American citizenship. And he responded by saying that he lied. You should know that it is not permissible in Islam to betray trust and break a covenant. Perhaps the brother was not aware of this. Please ask the brothers in Taliban Pakistan to explain this point to their members. In one of the pictures, brother Faysal Shahzad was with commander Mahsud; please find out if Mahsud knows that getting the American citizenship requires taking an oath to not harm America. This is a very important matter because we do not want al-Mujahadin to be accused of breaking a covenant."
...And he was also opposed to lying?! Who knew.