The Vulgate was not declared to be inspired. The Vulgate is trustworthy, ancient, and authoritative, that’s all. But being ancient and authoritative is plenty.
In general, the Church’s teaching is that all the authoritative versions of the Bible (like the Septuagint and the Vulgate and the ancient translations and the Dead Sea Scrolls versions, as well as the Masoretic Hebrew OT) are faithful translations of the Bible as God’s faithful people understood it. The inspired text of the Bible is not a single text from a single moment in the tradition. All the authoritative versions are part of the tradition being handed down, and therefore we pay attention to all of them, just as we would pay attention to the human teachers from their day.
If you went and asked various early Christian bishops whether their copy of the liturgical Bible readings included X or Y passage, some of their copies might differ on that. But in general, even the people without the passage would know the sayings and the stories in that passage. And now we have them too.