True, but the blanket condemnations of all books teaching the Copernican universe as fact were lifted in the early 1700's, after which point such books were freely published and read throughout the Catholic world.
I'm not sure why Galileo's book remained on the index longer. It probably had something to with its insulting tone and lack of tact.
The clincher, for me, that the "authorized" version of the Galileo affair is wrong are these words from Galielo's inquisitor:
"I say that if there were a true demonstration that the sun was in the center of the universe and the earth in the third sphere, and that the sun did not travel around the earth but the earth circled the sun, then it would be necessary to proceed with great caution in explaining the passages of Scripture which seemed contrary, and we would rather have to say that we did not understand them than to say that something was false which has been demonstrated. But I do not believe that there is any such demonstration; none has been shown to me."
That was written by Bellarmine in 1615. He died in 1621, a dozen years before the famous trial. Interesting letter, but not involved in the trial.