That's a joke answer, as you meant it to be trivially true for any curve family, but there is an important sense in which it is not true - Hobby splines are not closed under subdivision. So if you put an additional point down that lies exactly on the spline, then you won't in fact minimize the supremal difference (I assume you mean Hausdorff or Fréchet distance) to the original Hobby spline.
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Fun! Thank you :)
> supremal ==? something else
Yeah, I couldn't come up with the name as I was writing the comment and didn't want to splay a bunch of definitions across HN, hoping that "supremal" would evoke something kind of like what was in my mind.
In particular, I was imagining something closer to the Fréchet distance (allowing arbitrary indexing sets and not requiring continuity or anything nice in the reparameterization -- the infimum across all possible bijections (inf if there are none) of the suprememum of the set of distances between each bijected pair of points), but Fréchet, Hausdorff, and whatever that idea is called all have the same unique solution for this problem.