Periodic rekeying is like physical inventory or periodic password changes -- it helps you identify compromised assets.
Wouldn't the gang leader's radio get the new keys along with all the other radios? Yes.
I can't see how rekeying over the air is in anyway a good idea. It doesn't seem to stop any attacks but leads to failure modes. From my understanding, the new keys are transmitted over the air using existing keys. Thus, if your radio is off when the over the air rekeying happens, you don't get the new keys and thus can't talk to anyone in encrypted mode. This causes the fall back to clear mode and thus sensitive information possibly leaking out.
I turned it in, of course. They were really, really grateful.