Why does nitration of aromatic amines give meta directed nitro compounds?
A couple things here.  First, it's nitric acid, not nitrous acid, that is the nitrating reagent.  Otherwise, your own explanation is correct.  Orthocresol points out that phenols are sufficiently inert to protons, to avoid this situation.

Second, you can make ortho/para directed nitrated aromatic amines, if you are a little more clever and if you have a tertiary amine (http://www.chem.ucalgary.ca/courses/351/Carey5th/Ch22/ch22-3-6.html).  Use nitrous (not nitric) acid, which is weaker and will react only with the unprotonated amine.  That gives you a nitroso $\ce {-NO}$ group which you can then oxidize to the nitro group.