...allow private ownership of firearms. Browsing through the wiki article, I don't see a single one with a complete ban.
And the gun murder rate in Switzerland is not 0%.
I think the OP's claim is basically correct (some negative correlation between gun ownership and gun crime) but fudging the facts doesn't help the argument.
"Alas! I believe in the virtue of birds. And it only takes a feather for me to die laughing."