iirc its less about contaminating drinking water (there is a valve and pump to get through. rather tricky) and more about waste getting into dishwasher during cycle and you getting contaminated dishes.
my wife once decided to dump into garbage disposal a bunch of uncooked broccoli at once. it clogged garbage disposal and drain. when i tried to unclog it with plunger it backed into dishwasher (was hooked directly to garbage disposal bypassing airgap). took me hour to get everything out of dishwasher.
The airgap causes the pump to be physically incapable of backfeeding the drinking water supply with dishwasher waste