According to Tom Lehmann, the purpose of cross stacking the dough boxes with the dough balls (oiled) is to minimize drying. If this is not done, heat can build up in the dough boxes and can cause drying of the dough balls, along with trapping moisture in the boxes and resulting in water in the boxes on the following day.
From what I have read, the dough pans you refer to are an alternative to dough boxes or trays where space is not readily available to store the dough balls in boxes or trays, or where only a few dough balls are to be made. The dough pans are also usually designed to be deep enough to allow ample room for the dough balls to rise and to be conveniently stacked one upon the other without taking up a lot of storage space. I imagine that one would have to leave the dough pans unstacked for a while to accomplish the same objectives as using cross-stacked dough boxes, i.e., to minimize heat and moisture buildup in the dough pans.