On the left you can see the three boxes with their sides sanded flush and the lid nearly cut away using the table saw. Cutting the lid almost through is critical to a uniform cut as the article suggests. If the lid were to separate from the rest of the box you would have an awful lot more sanding ahead of you to get both the top and bottom pieces to meet flush.
One of the critical parts of this step was to make sure the box sides were sanded completely flat. I was able to accomplish this by placing a sheet of sand paper on a hard work surface and sanding the entire side at once. My belt sander was ok for the initial 80-grit sand, but the finer grits needed the entire surface to make contact with the sand paper at once.
Here you can now see the lid separated from the box bottom. Just a small (but sharp) hobby knife if all you need to separate them. A bit of sanding on both the bottom of the lid and the top of the bottom piece and your all set.
Here are the lids again separated from the box, but here you can see the hinge mortises I cut to hold the small box hinges.