A good litmus test is: did their gender make the violence worse than it would have been had they been the opposite gender? If yes, the violence was probably gendered. If not, then it probably wasn't. Compare a school shooter that shoots everyone, versus a school shooter that targets only women.
Let's say that the government of Ontario is interested in reducing health care costs. They have a hypothesis if there are more smokers, there will be more people diagnosed with lung cancer. So they look at the data and find that, while the number of smokers in the province has been decreasing steadily, the number of people diagnosed with lung cancer has been increasing. According to your logic, that means that the number of smokers does not cause an increase in the number of people diagnosed with lung cancer. But what if what actually happened is that people started getting tested more frequently for lung cancer, or that there was an improvement in the tests that detect lung cancer, so the numbers were going to rise anyway? Unless you control for other variables, it's really hard to make a judgment call.
Now, in the hypothetical situation where you only have X (gun control) and Y (violent crime rates) changing, and there are no Z (population), W (economy), A (political climate), D (weather), F (wealth disparity), P (inflation), Q (gun availability in nearby states), or T (number of police in the neighbourhood) factors fluctuating to complicate things, then, and only then, can you say that X and Y are in fact negatively correlated, and that an increase in X does not cause an increase in Y.
The point I'm getting at is that things are more complicated than the simple independent-dependent model that you seem to be pushing.
Consider my household growing up (I know, I know, plural of anecdote is not data, but this is just an example). Growing up we always had two vehicles - one minivan, and one smaller sedan. This was mostly fine - my dad took the car to work, and my mom had the van for driving the kids around, doing groceries, etc... The sedan got much more use, and the van mostly stayed in the driveway, except when it needed to be used for something a sedan can't handle. But when my mom went back to work, the van had to be used for the daily commute. And this eats gas like crazy. You shouldn't be driving a minivan with only one person in it, but because we couldn't afford a third car (a sedan to get my mom to and from work) and because we still needed the minivan for groceries & family trips, a huge amount of gas gets wasted hauling one person around.
However we're talking about people who have been judged by a jury of their peers.
No we're not. We're talking about people who may have been judged by a jury of their peers. They also may have accepted a plea bargain.
When Toyota says that they chose Canada over the US because of health care reasons, I'm heavily inclined to believe them. After all, with its larger population, surely the US has a higher number of highly skilled technicians to work for Toyota. But instead, they chose to add another plant to Canada. I'll leave you to reconcile the facts with your rhetoric.