With one term it gets more robust in the face of excluding endpoints when constructing the jackknife train/test split, I think. But you're right, it does sound fishy.
What the post is describing is just ANOVA. If removing a category improves the overall fit then fitting the two terms independently has the same optimal solution (with the two independent terms found to be identical). MSE never increases when adding a category.
This is why you have to reach to things that penalize adding parameters to models when running model comparisons.
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