I thought that was the case as well. Kapustin contradicts the Wikipedia article which cites the biography Prokofiev: From Russia to the West 1891–1935, which says Prokofiev was originally intended to study with Goldenweiser but it fell through. He also contradicts this article:
https://interlude.hk/on-this-day-23-april-sergei-prokofiev-was-born/ I found which says Goldenweiser declined to take Prokofiev as a composition student.
YT (author Yana Tyulkova): What about Prokofiev?
NK: Goldenweiser and Prokofiev knew each other very well and Prokofiev even took a few
composition lessons with Goldenweiser in his early years.
YT: I can’t believe!
NK: Yes. Then Prokofiev’s parents decided to find the real composer for their son and
Prokofiev started to take private lessons with Glière.
YT: So, Goldenweiser liked Prokofiev’s music?
NK: As you see, we played Prokofiev sonatas. I think Goldenweiser considered Prokofiev
as his former student, that’s why.
I'm interested in reading the Prokofiev book now. Kapustin's comment about the 'real composer' clarifies that Goldenweiser was considered a piano/keyboard professor first and foremost but did give Prokofiev his first composition lessons and still had a lot of fond sentiment from that. Prokofiev met Gliere at age 11, so Goldenweiser taught when Prokofiev was even younger than that. In this section they're talking about Goldenweiser organizing recitals by his students based on specific composers, and how he chose to do one for the Prokofiev sonata cycle.
