Yes, it's true that copepods will grow in the main tank as much as they will the sump or refugium. But the issue is that their populations can quickly be completely consumed by mandarins and other fish. That's why people talk about needing a large tank with a lot of live rock, plus limiting the number of copepod eating fish in the tank. With that approach, you're basically figuring that the mandarin can't get all of the pods and the ones that survive can continue to multiply.
The refugium/sump helps by providing a safe place for the pods to keep multiplying without predation while continually releasing some back into the main tank.
Some mandarins can be trained to eat other stuff as well. Search for some of the threads about people training mandarins. Reportedly the captive-bred Biota ones are brought up eating frozen food as well.