The 1 cup of quinoa that you added to the start contributes the final missing cup (its packing ratio does not change much, it's just the water that changes its packing ratio).
No, the difference is that at the beginning there is water between the packed dry quinoa grains, while at the end there is air between the packed cooked quinoa grains. That air is the missing cup.
Actually that can't work, the cup of quinoa has air between balls as well. It does have less air because the volume of the balls increases, but the math has to be done from scratch.