They state that they take charge and own the streets. I don't know what they take charge over. They certainly wouldn't take charge over the mayor or the fire chief, should one of them be walking down the street during their shift. That's the question that needs to be answered. We do not live under anarchy, where the one with the greatest numbers or the largest weapons wins.
Some people get really offended.
Apparently, walking down the street during their shift is sufficient cause for questioning, but they're mistaken. Perhaps you argue with the police for questioning you for no apparent reason. Nothing, other than you've offended them by asserting your 1st and 4th Amendment rights. As long as the police lack reasonable suspicion that you are involved in criminal activity, they should not be questioning you as to who you are or as to what you are doing. That's the 4th Amendment.