That still isn't true. I can play Ashe, Caitlyn, Draven and Sivir just fine, but I'm a horrible Ezreal player. They don't play the same and, while their job in teamfights is roughly the same, their execution in teamfights and their role outside of teamfights are very different.
My honest suggestion is to own all the champs you are comfortable with, as well as the flavor-of-the-month "OP" bans, so that you can trade them to those who might need them. Malphite, Amumu and Blitzcrank being the most obvious. Some will tell you Shen and Alistar.
Shen, in my opinion, is terribly easy to counter until you get to extremely high Elos, where various strategies beyond "teamfight after first turret falls" are more well understood. His global presence is what makes him dangerous in low Elo play, but it's easily avoidable if you just stay aware that he can show up at any time except when his ult is on CD.
Alistar, on the other hand, is inexplicably still banned. He was being banned in Season 2 because of his incredible ganks, but he can hardly make it out of the jungle alive in Pre-Season 3. As far as Support Alistar goes, he's not much different in lane presence than Taric or Leona.