That is also true. I think it's worth noting the US is basically the only country where such individual municipalities have such control over their individual police forces, not every little quaint village in Britain has its own police force for example. This also results in towns that are basically just speed traps and the like. Of course going the opposite route makes Joe Arpaios more of a problem, but if the state and oversight do their jobs (which they aren't in Arizona), that can also be dealt with.
Until now, it's been the same in Mexico. But they are trying to get rid of it.