Small generators rarely have emissions control systems anywhere near as good as the main engine (and it most cases, far worse). They usually have a completely open-loop fuel mixture control: a carburetor set to provide an adequate air/fuel ratio when the fuel tank is half full.
So, saying that only the generator is running isn't a very effective way to argue that these trucks are low-polluting.
While sometimes true, have you looked at some of the more modern portable and inverter generators lately? A Honda EU2000i can run the electrical needs of a typical food truck for an entire shift (~5 hours) on 1 gallon of gas.
So, saying that only the generator is running isn't a very effective way to argue that these trucks are low-polluting.