The lack of a surface mounted air gap (anti-siphone valve) usually results in some controversy. I will try to explain the need for this device as easy as possible. A surface mounted valve (air gap) is usually chrome in color, (other colors are available), that is mounted on the top of the counter near the kitchen sink. The lack of this device can create a potential health hazard due to contaminates that originate in drain pipes, drain trap, or the garbage disposal from siphoning back into the dishwasher, and because the water supply to this appliance enters level to, or below the drain line, it is necessary to prevent cross connection, or back siphoning which could allow drain water to mix with supply water. One can imagine the health risks in any one of these events.
Most of the newer high end appliances have a built in anti-siphon device or integral backflow device that is connected to the drain hose from the dishwasher, and is clearly visible inside the cabinet under the kitchen sink, and an additional air gap on top of the sink may not be necessary, Miele being one of those brands. Manufacturers installation instructions should always be followed. If the installtion instructions indicate that this device is not needed because of the factory built in valve, then that is what dictates whether a surface mounted device should be present. Local building departments do have differing views of these built in devices as to whether they are accepted or not, and I recommend referring to installation instructions, and inquiry with the governing building department in regards to their specific requirements.