The various extant Greek manuscripts available in the 16th century disagreed with each other. The Latin Vulgate was translated at a time when better manuscripts were available. It is a presumption on the part of the author that reading in Greek rather than in Latin made a difference in the decision making. The eastern Church, which never used Latin, did not buy into the Luther/Calvin approach.
What is most perplexing is that the argument between the Protestants and Catholics came down to the deciphering understandings of the 29 books that the Catholic Church decided would compromise the New Testament. Had the Protestants attempted to revisit and revise Canon and examining the many other works contemporary to the 29 chosen the argument might have been more about the message of God and less about political power.