Also, chopping off Hershel's leg would have not saved him. Our hearts pump 6L of blood per minute! By the time the leg came off the virus would have already well circulated well beyond where his leg was cut off. So basically once you are bitten, you are pretty much SOL.
I also thought this as well...I'm not sure how much it goes against previously established facts about what happens to a person when they are bit by a zombie, but perhaps it does not come as a result of any type of 'zombie active virus' entering the bloodstream. The zombie bites a person and they are infected in the cells at the point of the bite. Similar to gangrene so if you cut it off/out before it spreads beyond a point the person is then saved.