Coincidence. That Ethan W. was killed by Spencer.
So many reasons...
Zombies cannot be killed without a bullet to the head. The police were not aware of this and considered them crazed or diseased people, expecting them to react the same way.
Another reason is the circumstances of the outbreak. It is important to note that it was a mass outbreak at Warren Stadium that truly sparked the incident. A massive horde of Zombies swarmed the city and most of the first responders, including Deputy Chief of Police Raymond Douglas, were killed.
Chief of Police Brian Irons also intentionally stifled the force's attempts and made things much more difficult through absurd reorganization of firearms and ammunition, security measures, personal hunting, etc.