Typically, Plumbing Codes do call for a air gap device to be installed on the outlet of a dishwasher. However, many localities allow running the DW drain line up as high as possible up under the counter top and then running down to the disposal. Ive been doing this for years without problems. The air gap device is a real hideous thing to have on a countertop, in my opinion. Also, I doubt that the pump failure was due to back up. DW pumps are generally not known for their high quality…