DVT Ground Controller described a confused IFR release event when accurate coordination with the Local Controller failed and a takeoff clearance had to be rescinded.

Narrative

I was working Ground Control/Flight Data/Clearance Delivery (GC/FD/CD) while a trainee was assigned to plug in and monitor the LC-S Controller. The LC-S Controller was using the Trainee to coordinate IFR departure releases with me. I acknowledged the Trainee's request for releases; subsequently the Trainee would acknowledge my coordination of released or hold for release after I made the request to the IFR facility. I made my announcement out loud so the LC-S Controller could hear; but only the Trainee would acknowledge me. I request release of Aircraft X after the Trainee gave me the strip and asked for released. I gave the strip back to the Trainee and said hold for release. The Trainee acknowledged the coordination and I heard the LC-S Controller tell the aircraft to expect delay because the aircraft that just departed was also an IFR aircraft. Approximately 7 minutes later I got distracted with GC/FD/CD duties and heard the Trainee excitedly say 'no; he hasn't been released.' I saw Aircraft X on the runway preparing to align itself with the runway. The Trainee turns to me and asked 'he hasn't been released?' I reply 'no; he hasn't been released.' The LC-S apologizes to the pilot and directs him to exit the runway. The LC-S Controller says 'oh; I thought he was released.' I never implied to the LC-S Controller or the Trainee that the aircraft was released. Approximately 2 minutes later the release for Aircraft X came on the landline. Due to my attention on other duties; I would have not caught the LC-S Controller's error and I believe he would have cleared the aircraft without IFR authority. Subsequently giving himself and myself an operational deviation with the IFR facility. LC-S Controller should pay attention and not hear things that were never said. The strip wasn't even marked as released; at least not by me. Not sure where he got the idea that the aircraft was released.