Is dynamic champion banning broken?

I have been playing League for about a year now and really enjoy the game. One thing I'm wondering is if the banning system is broken? What I mean is that every time I have to ban, the champs I prefer to ban are always in the same position. For example Zed is always on the bottom second to the left. After reading about the ban system am I to believe that the other team have all champs available to them. It just doesn't seem right. Anyhow thanks for your time.