It is NJA policy that all dispatchers hired must be part 121 licensed. Once hired, you are technically not using that certificate - but you could loose it if found negligent by the FAA for some reason, same as you. You don't necessarily have to use it to loose it. It would be like loosing your pilot certificate by getting caught driving a car drunk - you don't even have to be employed as a pilot to loose your pilot's certificate. Same here.
Don't forget, when our plane went up in smoke in Leaky the FAA pulled the dx release and questioned the dispatcher also, during the inquiry. He was not allowed to release any more flights until FAA allowed it just as the crew was DNIF until allowed to fly again.
Actually the PIC has final release authority. Dispatch sends a conditional release for the PIC to review. Once PIC signs it, it becomes the final release, thereby fulfilling the dual-release system. Both retain operational control and can ammend, cancel, divert, or call an emergency at any time. ACP's, CP's, DO, ADO all have operational control also and can override the dispatcher but must assume responsibility for the release. In the history of NJA dispatch, I haven't seen this happen in a case where the dispatcher threw the safety card.