The American Society of Composers, Authors and Publishers (ASCAP) is a non-profit performance rights organization that protects its members’ musical copyrights by monitoring public performances of their music, whether via a broadcast or live performance, and compensating them accordingly. ASCAP collects licensing fees from users of music created by ASCAP members, then distributes them back to its members as royalties (BMI has a similar method for its members). In effect, the arrangement is the product of a compromise: when a song is played, the user does not have to pay the copyright holder directly, nor does the music creator have to bill a radio station for use of a song.
ASCAP attracted media attention in 1996 when it threatened Girl Scouts of the USA and Boy Scouts of America camps that sang ASCAP’s copyrighted works at camps with lawsuits for not paying licensing fees. These threats were later retracted.
ASCAP has also been criticized for its extremely non-transparent operations, including the refusal to release attendance records for board members, the notes from board meetings, and the reasoning behind their weighting formulas which determine how much money a song or composition gets paid for use on TV or radio.
This means that as an ASCAP member, you can expect a royalty every time one of your songs is played on the radio, at a public event or even covered by another performing artist, whether it is a major rock band in a stadium or a cover band playing a gig at the local nightclub. Of course, this is dependent upon the radio stations and nightclub owners paying their ASCAP fees and ASCAP has plenty of agents and lawyers running around to make sure that happens. Even if you own a small restaurant and you play ASCAP licensed music for your patrons, you will eventually be paid a visit by ASCAP to ensure you are paying the appropriate fees.
To my knowledge, an ASCAP member (like Heart) cannot for example tell ASCAP to license their music to everybody except for Rush Limbaugh, the RNC and Sarah Palin. The entire purpose of ASCAP is to simplify the royalty collecting process, not complicate it.
So if Heart feels this strongly about the issue, they would need to leave ASCAP and thus "unlicense" their music accordingly. By doing so, they would also forfeit ASCAP royalty payments.
That would be unworkable. Think about all the venues, songs & songwriters involved. There's no way that you could 'pre-authorize' song performances.