This is the logic that almost all gun control advocates try to use:
"Gun control reduces gun violence. Country X has gun control and low gun violence. Therefore gun control reduces gun violence."
This is the Post Hoc fallacy. There's nothing that suggests the gun control is the cause of the low gun violence.
Now I will rebut such a train of thought by flipping it on its head:
"Lack of gun control laws does not cause gun violence. New Hampshire has little gun control legislation and low gun violence. Therefore lack of gun control legislation does not cause gun violence."
That's logically sound because I'm simply refuting a single claim instead of making statements about a whole culture at large.
It's true that many gun advocates make the same mistake:
"The only policy that effectively reduces public shootings is right-to-carry laws. Allowing citizens to carry concealed handguns reduces violent crime. In the 31 states that have passed right-to-carry laws since the mid-1980s, the number of multiple-victim public shootings and other violent crimes has dropped dramatically. Murders fell by 7.65%, rapes by 5.2%, aggravated assaults by 7%, and robberies by 3%."
... is an actual example used by this website for the Post Hoc fallacy itself. But as long as you keep your arguments focused there's no need to make these sorts of claims. Refuting 'anarchy in the jungle' is good enough.