Jimbo stated the facts, to the tee. And yes, they do high loop the drains on the sides of the dishwasher now, the reason for interconnecting corrogated tubing (2)
Check valves can fail instantly, just like plumber1 stated with something as simple as a toothpick, chunk of food, shrimp tail. Lost all of its protective features, you cannot access it easily to clear it, springs can and will fail. Anytime you offer the free atmosphere (Air Gap) as a way to prevent backflow, it is a remedy for a simpler protection.
plumber1 I was referencing to wastewater from the kitchen sink, not on the potable water side of protection. That possibility can happen but my point in Air Gaps are to keep wastewater, meaning everything that DWV system has in it, like human feces, laundry wastewater, detergents, wastewater from sinks, tubs, showers OUT OF THE DISHWASHER. These are contaminants that affect human health. Very rarely do you see the kitchen sink on a separate line....other than gray water systems. Lots of bathrooms above kitchen sinks or one floor above, all tied together somehow or another. But what you mentioned is possible with the reversal of contaminates heading back towards the dishwasher in "certain" chains of events.
As to your response hj, It is not true that all dishwashers have check valves in them, I can simply deter that logic by buying OEM replacement hoses for older model dishwashers. Jimbo is correct in what he is stating.
In regards to high looping already being done on the dishwasher itself, Jimbo is once again correct. Proof is waiting at your local appliance store, start with Whirlpool, Kenmore, Jenn-Air models. Not all, but a good deal of them are making dishwashers this way. I've installed 3 in the past month, all three had dual hoses with one connection underneath, one to the drainage system.
A DW drain connected directly to the disposer is not "connected directly to the drain system".
Find me 10 plumbing inspectors in individual states that will sign off to that statement. Even better, have them call me.
The grinding chamber of a disposal beneath the flood level rim of ANY sink is not considered a threshold for the "CL" Critical Level.