box lid question

I recently bought Doug Stowe's excellent book on boxmaking. I've read through it quickly and now I'll start over, but there was one recommendation that I didn't really understand. When making the gallery for a lift-off lid (for a box made in one piece and later cut into lid and bottom) Stowe recommends cutting a dado on the interior (before assembly) and making the cutoff cut midway through this dado, so that both lid and bottom have a rabbet. He then recommends that the boxmaker cut, miter, and glue thin stock into the lower rabbet, to stick up past the cut and key the lid. I hope I'm stating this clearly; Stowe did a much better job of explaining. Anyway, he recommends this over cutting the gallery directly into the box top and bottom. I've been dadoing the inside, and then cutting the box apart on the router table, with the bit set further down the outside but overlapping the interior dado slightly. This forms the gallery at the same time the box is cut open. If you're careful with the bit height, the fit is perfect, with no sanding. I temporarily hotglue scrap pieces into the interior during assembly to keep the box from falling apart prematurely and messing up the router cut.
Could some knowledgeable person explain why Stowe recommends the technique he does? Thanks much.
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