Of course it has a shiny model. But it might be what they call "legendary locked". Where their shiny form is incapable to be captured in the actual gameplay, and therefore can't be used in tournaments or online play at all.
The only way to get them and play them online are through certain events or wondercard hacks. And not every "Legendary Locked" Pokémon has an event ticket. For some reason nintendo makes the models just in case? I don't know.
Not saying you are wrong about Ash's Greninja though.