I'm pretty sure if it is played on TV, you do. It's called a Synchronization and Performance license. The publishing company can deny such a license.
It's different than recording a cover on a record--that's called a mechanical license and it's automatic by statute. Also "grand performance" rights give you the right to sing someones song in a public performance (but not on TV). It's possible that, since this is a newsworthy event, the media is able to transmit the event under fair use. So the grand performance rights would give the right to play the song at the convention and the media would have a separate right to broadcast anything that happened there.
It all depends on who owns the publishing rights to Heart's "music." I doubt the girls own it--its probably the publishing company associated with the record company that Heart recorded for.
Take all this with a big grain of salt. It's been more than ten year since I practiced law and there's a new copyright act since I was acquainted with the field.
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.