The Galileo story is even funnier when you consider that the Church damn well knew that heliocentrism was probably "scientifically" correct, since they were already using that model to figure out Easter (Copernicus explained the precession of Mars better, and his model was more accurate than Ptolemy's).

It was the usual suspects, the Unwashed Masses who thought the Earth was flat and the centre of the universe. The Church apparently wanted to spread the news their own way - ie, to "control the narrative" so that the herd wouldn't be ... spooked, or whatever happens when universe-changing information comes along. Galileo was jumping the gun, and the Church didn't trust the People not to lose their nuts over the news.