For a commercial enterprise to use copyrighted material for anything other than parody, news, reviews, etc, permission must be sought from the owner of publishing rights (publishing rights are a license from the owner of the creative copyright), and a royalty paid to the publisher for a use license. Often (particularly with up-and-coming artists, very old music by more obscure artists, or deceased artists whose estates just collect royalties) that is an academic matter - pay the royalty and use the music. Permission is implied in the payment.
But in an instance where a band is huge like Rush, it is more complicated. Bands that big will often self-publish. They own the creative copyright, set up a publishing company, transfer creative copyright licenses to that self-owned publishing company, and thus own the rights to everything. Other times, an established artist will have the "muscle" to stipulate in the publishing contract that the publishing company does not have the authority to issue licenses without permission from the creative copyright owner.
So without a doubt - but admittedly without knowing the specifics in this case - Rush has the legal authority to force Rush to stop using Rush. I can't imagine it being otherwise. A band can't be successful for that long without gaining the needed muscle to have control over their own music.