As is usually the case with these sorts of things, this "theory" has been demonstrably disproved countless times throughout history - and yes, even our own American history.
Well over a century ago, Mark Twain wrote with utter disgust about the American tradition - imported from Europe - of young men settling petty offenses and disagreements by dueling. But the tradition stretches back many centuries, and provides innumerable examples of just how wrong the sentiment that "an armed society is a polite society" is.
After all, if every time you offended someone you could be called out to defend your honor in lethal combat, surely that would instill in people a sense of propriety, patience, politeness, and calm?
Yeaaah... about that... it turns out that humans are emotional, irrational, violent creatures - especially when someone who disagrees with them threatens to kill them over their differences.
Weapons do not make people more polite - they make people more dead.