I haven't read that but "gun death rate" is not the same as "gun crime rate"... Of course I expect guns to be used more in areas where they are available. Many legitimate self-defense cases are imperfect as well, and technically count as crime for BS reasons. Gun suicide rates probably would be higher with more guns owned by the public.

In summary, I don't think you are right and I would still support broad gun ownership rights even if you were correct about per capita. I am more worried about the public not having guns than having guns.