Could zombies ever be real?

Zombies, ah the wonderful idea of smashing in the undead's skulls being the only way to kill the,. Well, the possibility of a zombie apocalypse is low, but not impossible. Think of the pollution happening in the world, and disorders and diseases in the modern world. Also think of the disaster in japan. All the radiation leaking, the poisons and the water which animals drink and we hunt or fish. If one is to happen, I have a strong feeling it will start there. Someone could eat a infected fish, not realize what they have and end up transferring the virus to someone else. The only problem is, wouldn't zombies be shot right away? So why wouldn't we kill the very first zombies before it spreads? I say if something happens like this, it would take possibly days to take effect, so maybe a fever or flu that spreads normally and whips people out later in the time period of it. But I'm not sure.