Is this true? When the NT quotes the Hebrew Bible, is the Greek used in the NT identical to the Septuagint, or did they translate directly from the Hebrew?
It’s an overgeneralization. Many quotations are like the Septuagint, others seem to be built directly on Hebrew, and still others’ source text hasn’t been identified yet.
The NT is quoting the Septuagint. The popular OT in use today is based on the Masoretic texts, i.e. a 9th century Jewish canon compiled largely in reaction to Christian claims that the Old Testament Scriptures belonged to the Church. Martin Luther accepted or deleted books, based on a 16th century misunderstanding. When he was translating the Old Testament into German, he mistakenly believed that the oldest source for the Old Testament would be in Hebrew, so he found and used the Masoretic Text. In other words, the true Christian canon (including the “missing books”) had been completed 400 years prior to the Masoretic canon.