I can't read the study, but lots of cultures in the US attach stigma to suicide(weakness) and to gun accidents(stupidity). Families in these cultures sometimes feel that they share the blame for not properly securing the firearm or not effectively mitigating the suicidal ideations of a depressed family member.

Consider a family with a youth who accidentally shot themselves. Rather than state that it was an accident, the family tells authorities that it was a "suicide".

Consider a family with an adult that chooses to commit suicide. Rather than state that it was a suicide, the family tells the authorities that it was an "accident".