Perhaps it should read 'Arming citizens in the US reduces US crime' as there are many countries in the world that have unarmed citizens and far lower crime levels than ours.
There may be a cultural element to it, granted, but it's far from a US-only phenomenon. In many countries where the citizens' gun rights have been infringed, crime in that country rose and also became more blatant/aggressive than it had been in the same country when the governments rightly respected the citizens as their employers, rather than serfs.