I've read your response and can't understand it. Can't tell what you're expressing.
The only way an Air Gap serves its purpose is only when the device is above the flood level rim it serves. Any Air Gap open to the free atmosphere at the dishwasher (moisture, possibility of error in a concealed location) would be at a minimum, 2" below flood level. The "Critical Level" is the point at where the device may become submerged and backflow may occur. These are predetermined settings set forth by all regulating commissions.
Clipping the hose and high looping under the sink is the same as draining a pool with a garden hose draped over the edge, the end of that hose at a lower elevation to provide fluid dynamics to start the siphon process.
The first plunger to the sink drain and/or the waste level rising to the flood level rim at which the fixture will over flow, it will travel to the dishwasher.
Built-in check valves on dishwashers do not supercede local authority codes in the removal of an Air Gap.
An Air Gap is mandatory on all commercial industrial applications on the idea and premace of dishtank equipment, there is absolutely no reason the code should be relaxed down to the residential level just because the likelihood is less.
In my opinion in all that I've seen in my days as a plumber, the risk is higher on the residential level.