That study doesn't even say that. It doesn't propose causation, and looks at accessible firearms, not gun ownership. There's no way a gun kept in a safe or a nightstand reasonably affects your likelihood of getting shot, everything else being equal.
> We also did not account for the potential of reverse causation between gun possession and gun assault.
The study's methodology looks terrible. It's a case-control population study of Philly over 3 years. Every case began as a notification about a shooting case investigated by police. The vast majority of shooting data comes from shooting cases forwarded by police, not by sampling and then finding which of the sample were involved in shootings. As such, they excluded a valuable dataset of police-reported assaults that didn't result in shootings, which could have corrected some biases in the data based on how the cases came to the researchers' attention.
The 95% confidence intervals are wildly variable, and if you look at figure 3, any significant amount of lying by surveyed control subjects about having guns leads to insignificant results. If you call up some random gun-owner in Philly and ask them if they have a gun, how likely do you think it is that they'll lie? Those 4.x and 5.x odds ratios look impressive, but even after assuming 0% lying by case controls, they only barely clear the statistical significance bar.
It's difficult to speculate all the ways a study like could be flawed without seeing the underlying data and putting a lot of effort into analyzing it and how they corrected for potential confounders, but I'm not at all surprised they found gun possession correlated with increased odds of getting shot.
The causation determination really comes down to what kind of gun owner you are. There are a subset who own guns, carry guns, and do everything they can reasonably do to stay out of trouble, which often means avoiding friends or social environments that are generally "trouble". In that case, gun possession probably lowers your risk, because it makes you hyperaware of dangers and their avoidance. It's like a game you play every time you leave your home, of what can go wrong and what's the best way to handle it. Very quickly, that game becomes a habit and becomes uninteresting except when you do something or go somewhere unusual.
Then there's the subset of people who own guns and carry them because they're likely to get into trouble, they go around looking for trouble, or they go around oblivious to trouble. For them, maybe there's mild causation, having a gun makes them more confident to take more risks, or maybe there's no causation, and it's just the higher rate of gun ownership among those types (which includes criminals) that leads to poorly designed studies finding a statistical correlation between gun possession and getting shot. And there's no way to run these studies I've ever seen that satisfies both sides. Someone always thinks some study disregards something important.