Your'e correct. The Church in fact gave Galileo several passes. They even send him a letter telling him it's ok to work on his theory, but not to teach it as scientific fact. There were several reasons for this that never attention in modern anti-Catholic society. One was that Galileo's formula was WRONG. Though his theory turned out correct, his formula is still considered defective to this day, just as it was by most of his period peers.
The most notoriously erroneous charge about Galileo today is that the Church was trying to suppress science. It seems nobody can use logic anymore, because Galileo was taught science by Catholic scientists and professors. Galileo got himself into trouble because he became prideful and arrogant, he rebelled against authority and wrote stinging letters of attack against the Pope and cardinals, as well as against learned members of the scientific community. He refused every attempt at mediation.
He never was tortured in any way either, and his greatest 'ordeal' was that he had to stay under house arrest in the Bishop's manse where he studied and wrote until he became old. Some scholars say he was released long before his death. Leave it to the secular media and anti-Catholics to take this case and try to turn it into something it never was.
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.