Three issues here. First, the easy one . . . take Parkhurt89's advice and get the correct information from the source, which is CGO as a starting point. However, even then, I suggest you do the best you can to confirm what you're told with official sources (i.e., laws, regulations) by asking CGO the legal basis for their position. Not saying CGO will be wrong -- they're likely to be 100% correct b/c I'm sure you're not the first person to have this issue. However, I would not want to base my future on what an O-3 verbally tells me.
Second issue -- is there a reason you want to retain your non-US citizenship? If you plan to join the US military and commit potentially 24+ years of your life to it, why do you want to retain citizenship from another country?
Third issue -- lack of parental support for attending USNA. Yes, some mids successfully navigate USNA dragging their parents kicking & screaming behind them. However, it's also true that mids are typcially more successful at USNA if they have a supportive family. Or at least a family that isn't in strong opposition.
I suggest you consider why your parents are against your attending USNA -- is it because it's a military school and they fear for your safety? Is it because they have a citizenship issue? Something else? (none of my business, BTW --just suggesting you think about the reasons behind their views and whether their current opinion could change).
If they are so opposed as to not even wanting you to explore the idea, such as by posting on these boards, I fear you will have a very long & difficult road. Not saying you can't do it but, again, suggest you have a frank discussion with your parents about this issue. If you're truly committed, they'll find out eventually and it's better to air the issue now than later.