The airborne zombie-virus outbreak happens. Lots of people turn without being bit; other people don't. Do they ever explain why?
It can be assumed, however, that an undetermined number of original "outbreak" cases involved recently-reanimated zombies that were relatively intact and "clean". This could indicate that the active form of the virus does in fact play a part in the attack on the victim's system, perhaps by rapidly wiping out immunity cells which would allow for even weak infections to be deadly.
It has not been explained how and why the virus exist yet. The only thing we know is that everyone is infected. This means that it doesn't matter if you are bitten or not. As long as you die, you will turn in a zombie. The people that have turned have died, one way or the other. So far, we haven't seen any alive person to turn.
Rick's speech at Vol. 05: The Best Defense perfectly sums it up:
The second we put a bullet in the head of one of those undead monsters -- the moment one of us drove a hammer into one of their faces -- or cut a head off. We became what we are! And that's just it. THAT's what it comes down to. You people don't know what we are.
We're surrounded by the DEAD. We're among them -- and when we finally give up we become them! We're living on borrowed time here. Every minute of our life is a minute we steal from them! You see them out there. You KNOW that when we die -- we become them. You think we hide behind walls to protect us from the walking dead?
Don't you get it? We ARE the walking dead! WE are the walking dead.