“I believe Trent included something having to do with the mechanism, which is the part that the Orthodox didn’t embrace.”
The Western Church, GL, has tended to define theological points more precisely and legalistically than the Eastern Church. The reasons for this are many and include a different mindset when it comes to theology, history and frankly the challenges faced in the West, like the Protestant Reformation, which the East has never had to face.
We in Orthodoxy are content to leave certain things a mystery. Indeed, we formally call the the sacraments “Mysteria”, the Mysteries, because we honestly don’t know how they work but we have faith, even “knowledge” of a spiritual sort, that they do.
In any event, you put it just right. We don’t reject the Trentian mechanics so much as we don’t embrace them.
One thing to keep in mind with that statement is that the purpose of the Tridentine canons was not only the anathematization of the current heresies floating around Western Europe at the time, but they were also to correct many of the abuses that had been going on within the Church. That council was a true reformation.