Where I live (Finland) cops would have very little incentive to lie. We are brought up to treat each other in an egalitarian way, and that transcends most levels of our society. For example, in Turku stabbing[0] the police did not attempt to kill the suspect but to incapacitate him with as little force as possible. It's about how they are trained.
Police are quite respected, and not feared by anyone here.
Justice system is not about punishment, but about providing as low level as possible downside to illegal actions. So it's set up more like a statistical tool than like a personal punishment scheme.
Edit: I have to add, that while the general standards seem to be quite high, individual officers are not incorruptible. A head of drug enforcement was recently jailed for basically corruption. But the fact that anyone can be deposed if found wanting is perhaps a signal about the self repair in the system - individuals are corruptible, but the system and norms aren't. At least for the moment. Yes, a single officer might lie if bucketloads of euros are at stake, but a random officer would generally not lie for leisure. https://en.wikipedia.org/wiki/Jari_Aarnio
