No, their data is not that granular. They are just using a regression model per state to find the association between state-level gun ownership rates and state-level homicide data, e.g.
Quote:
Among male victims, each 1% increase in firearm ownership [across the state] was associated with a 1.2% increased incidence of firearm homicide victimization by an intimate partner and a 1.7% increased incidence of firearm homicide victimization by another family member [again across the state].
The data do not tell them specifically whether the victim's household had a gun, although I think the results suggest that it's likely a factor, i.e. because of the fact that they found a correlation for domestic but not non-domestic homicide.
It's true that they can't directly account for "violence avoided because the victim had a gun" (just like they aren't directly measuring gun ownership as a cause of gun homicide, only as a correlate), however it makes sense to think that if gun ownership helped people avoid gun violence then you would see a negative correlation between the variables, as you do in the last statistic I quoted for homicide rates involving strangers. So, indirectly, there is some accounting for that question.
I would guess the main avenue for criticism is going to involve the regression model, particularly this part:
Quote:
The SHR is limited by the fact that approximately one third of homicides reported by local law enforcement agencies to the Federal Bureau of Investigation are missing data on the victim−offender relationship. To address this limitation, Fox and Swatt developed a multiply imputed SHR to address missing data. The multiply imputed SHR applies log-linear models to impute missing case data and a weighting scheme for unit missingness to model annual homicide rates reported to the National Center for Health Statistics.
These kinds of techniques to infer missing data can work, but 33% of cases is very large, so I'd be worried about that. I assume we'd have to find the Fox and Swatt study to see if they've empirically tested the method used to infer missing data. That's potentially a big asterisk since error introduced via this model could easily overwhelm the correlation identified, and I'm not sure to what extent they can model that error in their confidence intervals. Maybe they can, it's a bit above my pay grade and I haven't read the whole study that carefully.