An action or state prior to another in a narrative sequence in the past tense is not automatically cast in the past perfect, especially with subordinating conjunctions that order a sequence by themselves, like after, before, once, until. If some action/state occurs between the two events, or if the completion of the prior event is topical, or even if the intervening time is itself significant, writers will frequently choose the past perfect. If one of these conditions is not met, then the verbs will usually remain in the past tense.
Compare these two sentences:
Ong’s works were not fully recognized until he left Los Angeles for New York in 1994, where he won recognition from Robert Brustein, the artistic director of the American Repertory Theater… — Miles Xian Liu, Asian American Playwrights: A Bio-bibliographical Critical Sourcebook, 2002.
It was not until he had left school, home, and Manchester that he began to change and grow. — AW Jones, Herbert Hamilton Kelly SSM, 1860-1950, diss., Univ. Nottingham, 1971.
The first sentence establishes a simple narrative sequence: the topic is the recognition the playwright received in New York after he moved there. Neither the move itself nor his former address is significant. The move bears no relationship to his recognition. It merely happened after the move.
In the second sentence, the author infers that Kelly’s personal development was limited by his earlier life in Manchester. His departure is topical, i.e., the act of leaving home, family, and birthplace facilitated this development. Thus the use of the past perfect.
If someone dies before some other event takes place, it can simply be a matter of “this happened, then that happened,” both events narrated in the past tense:
Dorothy Wrinch died before I went to Moscow; she never knew about my conversation there with Nikolai Vasilevitch Belov, Academician, past president of the International Union of Crystallography, Honorary member of the Mineralogical Societies of the USSR, USA, Great Britain, and France, Hero of Socialist Labor, … — Marjorie Senechal, I Died for Beauty: Dorothy Wrinch and the Cultures of Science, 2012.
I never knew my father's parents, they died before I was born. I never knew my mother's father, he died before I was born. But I really knew my grandmother. I spent as much time as I could with her. My grandmother was a rich old lady living in Brooklyn—or so we thought (about being rich I mean). She always bought us ice cream… — Helaine Krob, The Road Rises Up, 2002.
In both these sentences, neither the death nor any event in the intervening time is topical. In the first sentence, it’s the conversation with Belov; in the second, the memories of the author’s grandmother.
In this sentence, however, the author narrates the death of a half-sister whom he only knew from scant family lore. He also wonders if she ever existed:
Now, I knew that my mom had been married before she met my dad, but I was raised to believe that her little girl had died before I was born—as an infant or toddler. I don't imagine that I'll ever know whether the certificate is in error or whether I had a “half-sister” whom I never saw. – Jim Walker, Before I Go: My First Fifty-Six Trips Around the Sun, 2003, 20.
Because this unsatisfied curiosity is topical, the author chose the past perfect.
In this sentence, the author wonders about a long dead relative and recalls family stories about him. The death is in the past perfect and the lack of personal knowlege and family lore are narrated in the past tense.
At some point I voiced this idea and my father said, “No, they belonged to my Grandad.” My own grandfather had died before I was born so I never saw his face nor heard his voice. My parents often spoke of him and repeated remarks he had made. — B. Marie Mollohan, The Banks of the Holly, 2005, 1.
Since your example is a single sentence crafted as an illustration in a textbook, i.e., not “real” language with a context, it is impossible to say whether, were a context supplied, it would be more appropriate in the past or past perfect. The examples given here, however, sould give you some idea of which context goes with which tense: narrative sequence, past; topicality, past perfect.