Unfortunately, this problem is not entirely unknown in Germany, too. I have no idea how common it is, but there was one well-publicized case where somebody got beaten up by the police at a demonstration. The police claimed the man had insulted and attacked the officers and then resisted arrest. Video evidence the police had went missing mysteriously, but then volunteers started sending in the videos of the incident they had recorded, and the Chaos Computer Club (at least I think it was them) correlated all the recordings. The resulting video clearly told a very different story from the one the police had told. And I doubt this is an "isolated incident". When you cannot police officers to tell the truth about how they use the power given to them by the state, how can you trust them at all?
And just to be clear, my mother is a retired police officer, married to another retired police officers, so I have met my share of police officers, and all the ones I have met were decent people who valued honesty highly. But that makes the fact the police as a whole is willing to tolerate such behavior all the more troubling.