Is that really the case? I'd heard that the US did not technically recognize dual citizenship but other nations do. So wouldn't you technically be just a US citizen as far as the US is concerned?
That is really the case. Under international law, all "dual citizen" means is that there are two countries whose national laws consider you a citizen. The USA used to have laws against retaining your citizenship if you took out another one, but they kept losing in the Supreme Court, so stopped trying to enforce them in 1990. (I took out Canadian citizenship less than 3 months after that policy change.)
According to http://en.wikipedia.org/wiki/International_Traffic_in_Arms_R... that makes me a foreign national (despite also being a US citizen) which causes ITAR to apply to me.