In some departments that is true, but many cities are not this way: They will bust an off-duty cop for carrying as quickly as anybody else.
Plus, a cop in plain clothes has to be very careful about getting involved in police action whether it is department policy or not. Just a couple of months ago an off duty cop was shot and killed in Houston when he joined a foot chase armed. Another officer mistook him for a suspect.
Louisiana cops have even been known to bust Texas cops in uniform and on duty that cross the state line. Cops aren't super-citizens, and depending on how the law is written in a given locale there may not be a lot of difference between them and non-officers in terms of carrying and deadly force.
So true. My former office-mate was an ex-NYPD officer. He got shot by another cop when he was off duty because he got involved in a shooting incident at a department store. My friend jumped and disarmed a guy who was brandishing a gun. When the uniformed cops ran in, they saw him standing over the guy he had disarmed and, taking my friend for the attacker, shot him.