Bernie, using a cardboard box is not the same or works the same, but it can slow down the drying as there is only a limited amount of air in the box and with enough bowls or smaller box, the air in it will get saturated and so slows the drying, but that is where the similarities stop
With the brown paper bag the initial part is the same, the air gets saturated, a paper bag can also be closer to the turnings size, so less air, now the bag will absorb some moisture, and the turning can loose some more moisture, than the paper bag will have the air surrounding the bag take some of the moisture from the bag, and the bags inside air will give again moisture to the bag, the turning will then be able to loose some moisture again and this all keeps repeating till the moisture levels are the same all around.
The cardboard is not able to do the same as the brown paper bag, but it could maybe loose some moist air if the flaps are not fully closed, though it would be much harder to have a consistent process, as with the brown paper bags use.