Do you mean the slogan
"If guns are outlawed, only outlaws will have guns"
or "Guns don't kill people, people kill people."?
Both of those grate on my nerves because their sole intent is to obscure the direct relationship between weapon availability and crime. Sure there are some collectors out there who think guns are beautiful works of art that should be purchased and displayed under glass, but there are very few of them. The main function of a weapon, especially a hand gun, is to kill or threaten to kill.
Regulating screen names would not be like regulating a weapon that has a limited number of manufacturers (you can't generate it indescriminately like bathtub gin), requires each weapon to be identified by number, and requires each purchaser to be identified in person.
No, I don't think they are the same. But I must admit those slogans did pop up in my head even before you posted about it.