It's different than recording a cover on a record--that's called a mechanical license and it's automatic by statute.
Part of the rationale for the distinction is that putting a piece of music or song with visuals, or with lyrics other than those originally intended, may cause the music to be associated a message with which the composer or songwriter does not agree. A mechanical license only allows for 'innocuous' reproductions; if the person doing the recording wants to add his own 'message', a sync license is required and may be denied.
That having been said, many composers have signed deals with ASCAP or BMI. Those agencies have fixed payment schedules, and will grant performance rights on payment of royalty with far less concern for context than what composers who control their own copyright might express. If a composer signs with ASCAP, he forfeits control over his music in situations like this.
I think that's right. ASCAP and BMI license radio and TV. But not movies--I said it had been a while. So if McCain used it in a Gov. Palin movie documentary, he would have to get a sync and performance license. But ASCAP and BMI handle TV royalties. So if the documentary showed on TV, that's the performance rigts societies. And, of course, grand performance rights let you use the composition in a public live performance (a convention, for example).