DeRose doesn't say so explicitly, but the reason is that the position of any given point on the infinitely subdivided surface is only determined by the positions of a handful of points in the control mesh. That's why, for example, the derivation for the final position of B given at the end of the video only depends on its neighbors A and C, and not any other points.
Thus, if you want more control over a portion of a subdivision surface, you can just use a denser control mesh in that portion of the model. You can create arbitrarily hard edges by moving control vertices closer together. At a microscopic scale, the edge is still smooth and blobby, but it looks sharp at a distance.
You can also make creases in subdivision surfaces by using different subdivision weights over the surface of the model, which may be what DeRose is getting at when he answers with "magic numbers". But it's my understanding that most modern CG is done using subdivision with the standard Catmull-Clark weights over the entire model, instead relying on the density of the input mesh to specify detail.