You are absolutely right. The right was not claimed; it was assumed. In the 18th Century, with people walking around with swords on their belts, the right to carry weapons was not controversial.
I don't think swords were particularly concealed.
Certainly open carry was a common practice. While it would have been absurd to suggest that a gentleman with a sword in his belt be required to remove his belt and place it over his coat every time he went outside in cold weather, I don't know to what extent it was accepted for people to deliberately conceal weapons on their person.