This is true. I'm not sure about in public however. I would not be frightened if I saw someone with a sword.
As for walking around with a gun, most states that allow people to take their firearm out of the home require a permit to do so. The permit (often called a conceal and carry) requires the person to take a safety course, as well as a course on the laws involved, when you can and cannot use it, as well as a proficiency test so that if they ever have to use it they dont accidentally shoot the wrong target.
When there are situations with riots and gun violence in general, those weapons are usually not legally bought and sold. There is a massive influx of illegal firearms that enter the country every year, likely from the same trafficking that involves drugs. Our drug policy is another failed program all together.
If someone who legally owns a firearm is convicted of any violent act, even simple assault, even if it is not involving the firearm, they lose their firearm and any permits they have along with it.
Besides our constitutional 2nd amendment (the document is of a lot of importance in the USA) the other reason they are still legal to own, is that illegal ones have not been completely removed from the hands of criminals, or even close to it.
If someone wants to live in a country where only criminals are armed, there are a lot of places they can live.
I feel plenty safe living in an area where a lot of honest and competent responsible people are armed, as I have piece of mind that if someone pulls a gun on me, there will always be a good guy close by who can tell him to put down his weapon, and back it up with one of his own.
If it were possible to remove firearms from every bad guy, but as a condition I had to give up mine too, I would be fine with that and gladly hand it over. That is a perfect world scenario. I doubt we will ever see it come to pass, but in an effort to get there we should not be disarming the honest people first. That is the wrong order of events.