Why not given them the ability to fly and read minds also? They are ninjas after all.
Ninjas don't fly or read minds. Ninjas pwn with swords and nunchuks and the little stabby things on the card. And don't get caught. That's where the damage immunity comes in. Ninjas are not the only warriors with skills; you can't kill Chuck Norris either. But that doesn't make it any less ninja.
Edit: (just to prove my point)
In games, ninjas are usually high damage, low defense creatures with a stealth ability.
Stats: 7|5. Ability: Immune to damage and poison.