If the gun violence is massively higher, and that correlates with gun ownership, then maybe the two are connected?
You can't say the two correlate though because there isn't a nation with similar enough circumstances to the US to compare it to. If there were and gun violence were a problem in that hypothetical nation as well, then you might be able to say gun ownership is the problem.
That's why I lean more towards comparing violent crime rates in general rather than limiting it only to gun violence. It's a more fair comparison and it also goes a long way to show what impact gun ownership has on violent crime compared to nations without gun ownership. Looking at violent crimes statistics, there are several of Lexicus's vaunted European paradises that have higher violent crimes rates than the US. The UK being one of them with a violent crime rate of 898 per 100,000 compared to the US's 387 per 100,000. So it would appear that gun ownership doesn't really encourage more commissions of violent crimes.