Champs that go "invulnerable" don't actually go invulnerable
If your champ goes "invulnerable" then the champ should be invulnerable. In this ARAM game I was playing Fizz. In this clip you can see me get hit by a Kog'ma auto while I was in my Fizz E. I've also seen zed and shaco be hit my autos and abilities while ulting. Please fix the game. 
Edit: I messed up and it is untargetable not invulnerable. My apologies