Change one thing
A check refits a model after both dropping a different set of rows and changing the link. The coefficient moves.
Why can that check not say which change moved it?
Worked answer
Two things changed at once, and the coefficient is one number. The move could be the rows, the link, or both. A comparison that is about the link refits on the same rows. A comparison that is about the rows keeps the same formula and the same link. Recompute the rows, the unit, and the scale one at a time before treating the move as a property of the estimator.