True, but it is undeniable that mother Church overreacted. There was absolutely no justification for putting Copernicus and Kepler on the index, as well as keeping on the index a blanket prohibition of all heliocentric books until 1758.
I don't think they overreacted nearly as much as has been written by the anti-Catholic, revisionist 'historians', especially when you take into account that Galileo was countering the belief of the scientists of his day, and that of the entire Christian Church about the structure of the universe. One does not smash universally held scientific and religious beliefs without some strong degree of opposition, (especially when other renowned scientists are refuting him).
Cardinal Bellarmine wrote to Galileo asking him to merely refrain from publishing and teaching this theory until the Church had the time to investigate and understand it better. Also, if anyone is going to be fair minded about the matter, it's essential to understand that the best scientists of the times (correctly) believed that Gallileo's formulas and calculations were flawed.
Scientists today of course agree with Gallileo's heliocentricity, but it's now universally agreed that the 'proof' he presented for his theory was faulty. The Church was being advised of Galileos defective formulas by the best scientists of the times.
Galileo's troubles arose in great part from his own pride, arrogance, rage, and verbal venom spewed at the Church and at some of his academic peers. He was never asked to recant or drop his heliocentricity theory, but only to develop it privately. This is extremely understandable, because at the time Galileo was propounding something akin to a 21st Century scientist suddenly claiming that the earth is still and the sun revolves around it.
Universally accepted beliefs never die easily among human beings, and the Galileo story as it's presented by modern revisionists attempts to turn that fact of HUMAN NATURE into some sort of great flaw in the Catholic Church. Well the Church on earth does have a flaw as far as its members go, they are faithful believers but they are also imperfect human beings. Old Mr. Galileo was every bit as flawed as any member of the Church of his times was.
Galileo himself was probably relieved that the Church was patient and merciful with him; his great 'torture and imprisonment' consisted of being confined to the Bishop's manse, where he continued his studies and, (as many scholars claim), was eventually released.