Outside of big cities it gets even more lax. You just see police officers hanging out like regular people. I once saw an old guy get into an argument with the cops that looked like an argument between two people, not between "officer and civilian". In the US that wouldn't happen, the officer would feel slighted and probably arrest that guy, or the guy would never dare to talk back to a police officer in the first place.
But to your point I suspect the military police is very brutal.