Not so, reveals Rosanne Cash to CBS Sunday Morning contributor Russ Mitchell.
"I didn't want to sing because I thought that's what made you famous. And I thought -- that was a really bad life choice to try to become famous," Cash says.
She adds, "You know, obviously because when I was a child my father was very famous and he was -- had a drug problem and my parents' marriage was falling apart, and he was gone all the time. So I -- I associated all of that with singing, with performing. I thought, well, this is not good. This is not something you want to do."
Despite her initial doubts and beyond her famous surname, Cash has created a career on her own terms.
This past week, Cash released what is perhaps her most personal album to date -- and what might just be her finest: "Black Cadillac." It's a musical memoir of mortality, loss and redemption.
Cash explains that the album served as a catharsis.
"The writing of it was a release in a way," she says. "And so to bring my reason and discipline and my sense of poetry to this -- these feelings that something manageable, this tremendous sense of grief and loss, to bring all of those things to this, to this kind of tidal wave of feelings was useful to me."
The album charts her efforts to make sense of the recent deaths of her stepmother; June Carter Cash, her father, Johnny Cash, and her mom, Vivian Liberto Distin, all within a two-year period.
In the title song, Cash sings, "It's a black heart of pain that I'm wearing that suits me just fine. 'Cause there was nothing I could do for you when you were still alive."
Cash, however, admits, "You know, I don't feel that bitter right now. I felt that bitter when I wrote the song because my dad suffered for a long time with illness in the last several years of his life. And you know, I ended up feeling very helpless that I couldn't ease his suffering and I couldn't make him better."
It is a grief Cash has transformed into songs about past and future while taking a look into Cash family lore: a black Cadillac, an open road, a radio, a house on the lake, laughter and prayer.
Asked whether the process was difficult, Cash said no because, "it rhymes."
Cash elaborates, saying that "if I write these songs and I've brought, you know, 28 years of songwriting to it and I make it all rhyme, you don't know where I took poetic license, you know? You don't know what is fact and what is truth."
The eldest of four daughters by the legendary Johnny Cash and his first wife, Vivian, Rosanne was a latecomer to music, a self-admitted nerdy kid more comfortable in the world of books than at center stage. Eleven when her parents divorced, it wasn't until she was 18 that she learned to play guitar while accompanying her dad on tour.
It was a life-changing experience.