The thing is, he isn't a ninja. None of the people in Naruto really are, except maybe the Root members. However, they are only ninja by the loosest of definitions.
A ninja, like a spy, is someone who lives so covertly in their black ops, their participation and knowledge of that world is completely cut-off from civilized society. True shinobi, hashishin, Spetznaz, and SOG types perform their missions without any knowledge getting out about their existence, and their personal lives are so separated from their professions, it would be next to impossible to believe such a person is capable of being an assassin.
So, the concept in itself of a ninja village is completely insane. How could one have a village so open to the outside world that participates in clandestine warfare? That would put everyone in said village at risk from conventional warfare, which, if they weren't portrayed as a bunch of superheroes flying around without enough kryptonite in the world to stop them from wearing obscene mesh shirts with nothing underneath (I can only imagine how the cheese grater scars look on someone with breast augmentation), they wouldn't live very long.
You want to portray Naruto, Hinata, or even Konohamaru as a ninja? It's simple: you play Konoha off as a fully independent city-state within Fire Country, and keep any clandestine activities restricted to the Fire Lord's personal knowledge. All missions are paid outright to the village, not to individual teams, like government funding to a branch of the department of defense. Even knowledge of the team makeup is limited to the extent that Naruto would have no idea that Shikamaru or Tenten were, infact, genin.
As for the induction and training off new academy students, that would have to use the cover of a reform school, or perhaps a military academy for teaching conventional warfare, with that sub-category for clandestine operations that is kept rather secretive.