All of that is true, except for UA winning the slot today thanks to congressional pressure. If AA comes along and files, who would Congress pick? AA has more muscle with the Hill. None of that muscle was enough to win any of the original 6 slots.
Another thing that is true is that the largest carrier to receive a slot is America West. Awarding a DCA-LAX slot to UA would go against the DOT's precedent of awarding slots to smaller carriers, a.la Alaska.