That's partially true. They give you the flu virus, in inactive form, so your immune system can respond and create antibodies to the live virus "in the wild." You get the immunity, without getting sick; it's the best of both worlds.My parents, even when I was little, never let me get the flu shot. My father just said that they just "give" you the flu so your body grows immune to it.
In no way can you get the flu from the flu injection.