Kind of interesting. You assert that the authority which excommunicated Pelagius, had no authority to burn books.
What on Earth are you talking about? Pelagius was excommunicated in the 4th century. The Inquisition (which did even have temporal authority to execute and excommunicate, not just burn books, but not the eternal authority of infallibility) was only formed in the 12th century.
But one "ecclesiastical police officer's" authority is not infallible, and not even legally binding. A trial was also conducted to weigh the accusations, and Pope John Paul II did apologize for the misdeeds in the conduct of that trial.
None of which changes the fact that the trial's sentence included no punishment for "Copernicism," nor was it wrong and Gallileo correct on each key matter.