Okay, look at it this way - they all have the virus that turns them into Walkers when they die.
No matter how they die, as long as the brain is still intact, they will come back as a Walker because of the (I assume airborne) virus.
The bites infect them with a deadly fever. I mean c'mon, they're walking corpses, full of bacteria and all that jazz and are alive because of some crazy virus.
So anyways, the bites infect them with a deadly fever which kills people - and so then because of the other virus, they come back as Walkers.