Two of those rules are in place everywhere. Two cards must always be shown to scoop a pot in a showdown. Also, it is standard to have to show the rest of the table your cards if you expose them to one or two people. However, that third rule is CAZ specific. Most places will allow a player to show one card for an uncalled bet. The "show one, show all" term came from the first rule, having to show all players if you show one of them.
We had a no limit cash game going at sea while I was in the Navy and one guy thought "show one show all" meant showing both cards if you expose one...not only that, but he actually flipped over the player's other card. He almost got beaten up and thrown out of the game but he was such a donater, we let it slide.
When I first found out this rule at CAZ, I developed a technique for throwing cards into the muck and having one "accidentally" turn over. I stopped doing this as I figured it was an abuse of the policy and besides, I rarely have a desire to show a hand or part of a hand that isn't called. Their house, their rules, I suppose.