I can see what your saying.
During the... 5th book, I believe, when Harry starts teaching his friends how to defend themselves - how is that different than what we do?
Granted, they meet in a secret room, but nonetheless - they teach each other how to defend against some of the more prominent spells.
Something else to consider - every person who is capable of casting spells has their wand on them wherever they go. Even Harry, before he can legally cast spells away from Hogwarts (when the dementor pays him a visit in the park). So, by that nature - they all conceal carry.
Usually, the wand is used as a tool. There are several instances where Ron's mother uses her wand to make dinner, clean the house, etc etc. Of course, there are also those who use the wand as a weapon, and intend to cause harm with it - just like in today's world.
So, who knows? It could have been just some fairytale concocted on napkins while Rowlings worked in a diner, or maybe she really wanted to have some depth to it. That's something that would have to be interrogated out of her, or be left to the masses for them to *think* about what she *might* have *possibly* been trying to say (i.e., its more than likely a story, nothing more)