First, the rental right is aimed at works (movies and other works or software works). Whether the recorded concert is made into a CD, whether it is a film or a video product, is controversial.
Second, the singer is a performer and has no right to rent, and does not need the singer's consent. (If the singer is a songwriter, the songwriter has no right to rent songs, because the right to rent is only for film works. )
If the CD is a video product, it is not a work protected by the right to rent and does not need the approval of the radio station.
To say the least, if a CD is a movie or other works, you need to obtain the consent of the author who made this similar film work, that is, the radio station.
Lease rights have nothing to do with whether movies and software are genuine or not. If you buy genuine movies and software, you can only say that you bought this thing, which can be used by yourself or appreciated. You can't rent what you bought without the author's authorization.