It is similar, as you say, to a trap that is not vented.
A grease or kitchen waste interceptor can become "air bound" if the air in the influent pipe that is brought into the interceptor through the influent pipe cannot get out of the interceptor. The trapped air builds up and gradually the water level in the interceptor lowers, thus making the interceptor ineffective. Thus you have to trap the interceptor, either on the interceptor itself or on the outlet piping to let the air out. You also have to trap the drain to prevent sewer gases from entering the occupied space. Thus the "double trapping".
We design our interceptors with an open sanitary tee, inside the interceptor on both the inlet and outlet pipe. This opens the inlet, interceptor, and outlet to allow the air to flow up and down the piping network. Then we do not have to vent the interceptor.
In some jurisdictions that I have worked in, they require an exterior grease interceptor. This has its plusses and minuses. If it is located too far from the kitchen, then most of your grease never makes it to the interceptor. And it is also difficult to put these in for remodels of buildings in the middle of the city, which do not have room outside. The plus is that it can be more easily monitored by the AHJ to verify that it is being cleaned/emptied. I prefer them outside since the larger the tank, the more grease it can separate and hold. But I have never worked where the design conditions were that cold so I can understand the aversion to an exterior unit.