Were the Greek and Hebrew texts corrupted by heretics, leaving only the Vulgate safe?

That is absurd. There may have been some texts corrupted by heretics, just as they corrupt everything else, but the question is whether the Church caught them, and you do not catch them by making a translation; you catch the people who have misconstrued the Greek and Hebrew, and then you make the translation. The fact that people tried to get at the Greek and Hebrew, not the Latin, only shows the importance of the Greek and Hebrew, because those are the inspired languages; the Latin is a translation. The Douay-Rheims was not the first English translation; we had English translations as far back as the 900s, and when the monks copied manuscripts they were copying Greek and Hebrew, not Latin. Somehow Catholics think that because the Vulgate was endorsed by a pope it is the ultimate word of God, but it is not; there were six editions of the Vulgate after the first was said to be authorized. A pope cannot make a dogmatic, infallible statement about a translation like the Douay-Rheims, and he knows he cannot, because there are some five thousand Greek manuscripts that all have to be collated to arrive at the best possible inspired text, and we have it now with maybe one percent doubt about certain verses.