Iodide is present in very small amounts in C-41 developer and leaving it out will not cause fog; I have done so with home brew experiments. Leaving the bromide out can. The bromide is in part A along with the carbonate (buffer) and sulfite (anti-oxidant) and other ingredients and I believe the iodide is as well. In a replenisher, there would be less bromide or none at all. It would be in the starter, so fog could result without the starter, especially if the replenisher is mixed incorrectly, then used to develop film.
I have one more possible explanation, why less of part B can make the dev more active: HAS is quite acidic, so adding less of part B raises overall pH of the developer.