Yes, the theory is the bite kills you (maybe with an infection?). People get a high fever and die. The bite doesn't turn people, dying does. Everyone just assumes that a zombie bite turns you because that's the way most stories go, but that doesn't have to be the case.
It is clear that everyone is infected from the start, which is why there are so many zombies. How else would prisoners inside locked jail cells get infected? There's still some inconsistencies with some people turning right away while others don't of course.
.