Actually, they are correct. Looking at Cause of Death Statistics from WISQARS, years 2001 to 2012, the raw numbers of gun deaths have increased about 14% over that period, with a rate per 100,000 population increased at a smaller 2.5%. What they don't point out is that gun homicides have remained relatively flat over that period, and as the population increased, the rate of homicide per 100k declined by 4%.
The increase is due entirely to the increase in suicides. Gun suicides increase by 22% over the period with a rate increase of 10%; so, the rate of gun homicides has increased by 10%. Non-gun suicides, however, have increased by 44% in numbers over the period with a growth rate of 30%. Looks like suicide is a suicide problem, not a gun problem. The US suicide rate, even though it has increased, still ranks that behind the gun free paradises of Japan, China, South Korea and Hong Kong and behind the overly civilized Western Europe countries of France, Switzerland, Germany, Belgium and all of the Scandinavian countries, according to www.suicide.org. Looks like more guns do make you safer, at least from suicide. When I get some time, I'll compare gun ownership rate to suicide rate to see how the different countries rank.