If you’re arguing that the RC Church DIDN’T act as sole custodian of BOTH testaments, you’d better check it out, unless you mean that what became the Eastern (Orthodox) branches of Christianity shared some of the original texts for about 1000 years.
But if you’re arguing that the “Jews are entrusted with the oracles of God,” meaning that the Jews either shared or exclusively maintained BOTH testaments, you’ve greatly expanded what Paul said. For one thing, my bible says the Jews “WERE ENTRUSTED . . .” which, it’s fair to say, most Christians believe. The Jews, after all, have never laid claim to protecting the integrity of the New Testament. Secondly, Paul had no way of knowing that the Jewish religion would continue on its own path, without Christ, without the New Testament. He, the apostles, and nearly all their first followers were Jews who accepted Christ as the fulfillment of the (Jewish) Covenant. They had no intention of establishing a *new* religion. Christ, in their eyes, was the Perfection of Judaism, the Embodiment of the original Covenant, not the founder of new religion.
Obviously when Paul wrote his letter to the Romans the only Scripture in existence was the "Old Testament".
Though the Catholic Church and the Protestants have maintained their versions the "oracles of God" was, is, and always will be be entrusted to the Jews.
We do not need any Chriistian Church to maintain the Tanach.