This argument is trotted out every time the gun violence issue comes up, but there's no veracity to it. The data is freely available. It's been several years since I did this but I plotted gun ownership vs gun deaths per 100k population, by US state, from publicly available databases, and they correlate exactly. More guns = more gun deaths, full stop. It's not a matter of the data not being there to show this, it's more a matter of a really strong cognitive bias that prevents people from being willing to even consider the evidence that doesn't support their preconceptions.

[edit] the graph came out looking like this https://twitter.com/73rhodes/status/915604039873769472