The US gov doesn't seem to recognize whatever dictionary that came from. As I understand it, peace officer is a civilian who has been trusted by the rest of their society to uphold and enforce the rules and laws that we have created to keep our society civil. LEOs are civilians, period. Sure, there's a distinction between a regular civilian and one that is a sworn officer, but they're still civilians and any officer that thinks otherwise is sorely mistaken.
Put it this way... If a cop refuses to do what their boss tells them, they get fired. If I refuse to do what my boss tells me, I could be facing an Article 15, a chapter separation, a Court Marshall, and time in a military prison, depending on how serious the offense is. A cop can quit anytime they want. If I decide I don't want to do my job anymore, tough shit cause I'm govt. property. A cop answers to local and state entities. Military answers to the Dept. of Defense.
Also, that definition would mean that all the Nat. Guard and Reserve personell would be considered civilians, not military, and I'm pretty sure that's not the case.
ETA: The Oxford American Dictionary defines a civilian as anyone not serving in the armed forces. Says nothing about police, or fire departments, and makes no distinction between those on active-duty or reserve status.