This right here sums it up. The bonus HD advancement for animal companions as their druid gains class levels is not the same as gaining class levels themselves; those are just basic d8 animal hit dice.
Sure, sure. But they still gain bonuses to Saves (Good Fort/Ref, Poor Will), BAB As a druid with the same HD, and Feats. So it's, for all intents and purposes, the same as leveling up.
I kinda have to play Asmodeus's advocate here, as my player isn't present...