ASCAP is (almost) correct. While copyleft doesn't undermine copyright, it does undermine the copyright cartel. If artists begin to license worthwhile, popular, and (monetarily) successful works under copyleft -- if artists succeed while granting people more rights than they, strictly, have to -- then consumers might begin to wonder why more artists -- and big companies -- don't do that. Using copyleft could become a competitive advantage. And then how will Big Music justify restricting users?
If the sheep wake up, the whole industry -- as currently organized -- falls apart. And that's what ASCAP is worried about.