This is a silly myth. Killing/injuring a police dog does not carry the same penalties as killing/injuring a real human being. No such law equating a dogs life to that of a human being would stand up in any reasonable court room.
Right you are, as they don't seek the death penalty or life for police dogs. They do however still relate a police dog as a police officer and carry stricter punishments than if it were just a neighbors dog. Laws on this vary by state.