Pius XII did bother to explain in detail in Divino Afflante Spiritu what Trent meant by authoritative—but he also made it clear that Trent valued the original text more than the Latin—authoritative has a juridical sense, as Pius XII makes clear.
If one bothers to read Leo XIII’s 1893 Providentissimus Deus one can see that the value placed on original languages is not so modern, a point further emphasized by Pius XI in the 1920 encyclical Spiritus Paraclitus. The myth that 1943 some how changed everything was dreamed up by “scholars” in the 50’s and 60’s looking for an excuse to ignore the entire history of the field. Pius XII made very clear both in DIviono Afflante Spiritu, and in Humani Generis a few years later that his scriptural teaching embraced the encyclicals of both his predecessors in their entirety.
Whatever the vote at Trent, it was sufficient and then signed by the Pope.
http://w2.vatican.va/content/pius-xii/en/encyclicals/documents/hf_p-xii_enc_30091943_divino-afflante-spiritu.html
If Latin was the only language available to the "greatest Doctors" then that partially explains part of the problems we see in Roman Catholicism.