They generally are.
Problem is there is a tiny little overlap in the middle of that Venn diagram, and that tiny overlap seems to be responsible for a great deal of problems.
I don't think there's nearly as many as you think. It's a perception bias, the few that there are stick out a lot because they are hilariously stupid so you read about them a lot and it seems common.
Keep in mind that in the US, about half the households are armed. And the half that own guns own enough guns to arm the other half. There's more guns than people in this country.
If they're truly was a significant overlap between very stupid people and gun ownership, the nation would be like a roadrunner cartoon with Yosemite Sam type a shootouts and people firing into the air on every street corner. That is seriously not the case.
Well, the chief of police in my city did this (accidental discharge of gun in the oven) once, so make of that what you will. He did have the integrity to discipline himself, per department policy.