That’s exactly what it’s for. If you block the sink drain and fill it with water, you can have water flow down the dishwasher drain hose and into the sump in the dishwasher. If that happens during the rinse cycle you’re rinsing with grey water.

That is exactly why they are required in restaurants. You wouldn’t want the sewage to back up into a sink where food or dishes might be.

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.