Don't shoot the messenger. That's the plot device in the novel, and so far, the tv show is following the plot fairly close.
Death, by any means, is the trigger. It's just that the bites are 100% lethal, and quick to enter the bloodstream.
The quote from Issue #41
"...the rule is: WHATEVER it is that causes the zombies, is something everyone already has. If you stub your toe, get an infection and die ... you turn into a zombie. UNLESS your brain is damaged. If someone shoots you in the head and you die ...you're dead. A zombie bite kills you because of infection, or blood loss ... not because of the zombie "virus.""
You can survive a zombie bite if you amputate the part that is bitten. Dale gets bitten, and has his leg amputated by Rick later on.