Plot hole for the Walking Dead?

Totally random thought that won’t fit in 140 characters… In most zombie movies, you get bit or scratched and you get infected and turn into a zombie. In season 2 we found out everyone is infected, you die you turn into a zombie. So why then, when Hershel was bit in the leg, did they need to amputate to prevent the infection from spreading? He, in theory, was already infected and a non-life threatening bite should not be cause for amputation.