The game seemed to establish that you become a zombie if you die (sans dying by shot to the head), not if you become bitten. I guess you do become a zombie also if you've been bitten? I don't remember the game establishing that, so I was very confused as to why being bitten at the end was a big deal.
The bite kills you because zombie-magic-poison. Then you come back because you're dead.
Well, it's not because zombies have special poison. It's because zombies are fucking disgusting and ridden with bacteria and disease. A bite or a scratch is like 20 different kinds of infections.