The interesting thing is that song writer and not the band receives the royalties of any particular song. In other words the song writer and not the band owns the rights to the song.
A band may not like who uses their rendition of a particular piece but as long as the royalties are paid to the song writer the band or the writers don’t have a legal ground to stand on...
Why do you think Elvis bought the copyrights to any song he sang? Dolly would not sell him the rights to one of hers and reaps plenty of royalty checks from those she grants permission to sing it. Even Whitney had to pay to use the song. ‘I Will Always Love You’ after discovering that she would have to sign over half of the publishing rights for the song if Elvis did it. Dolly has brains for business.