His quote from Cardinal Bellarmine sums it up:
If there were a real proof that the sun is in the center of the universe, that the earth is in the third heaven, and that the sun does not go round the earth but the earth round the sun, then we should have to proceed with great circumspection in explaining passages of Scripture which appear to teach the contrary, and rather admit that we did not understand them than declare an opinion to be false which is proved to be true. But as for myself, I shall not believe that there are such proofs until they are shown to me."Cardinal Bellarmine took the reasonable position that he would accept Galileo's theory once convincing evidence was provided. Galileo had the correct answer, but little evidence. Today, we would categorized his view as a "theory," which is what the Church at the time did.
Moreover, Galileo wanted the Church to promote his theory as established fact (which is outside the purview of the Church).
+ + +
But the author leaves out some important facts regarding Copernicus. Not only were several cardinals supporting Copernicus' research into heliocentrism, they helped to fund it.
Copernicus dedicated his book, "On the Revolution of the Celestial Orbs" to Pope Paul III, in the hope that the Pope would protect him from antagonistic astronomers and Protestant revolutionaries, or "reformers."
Nicolaus Copernicus dedicated his most famous work, "On the Revolution of the Celestial Orbs," in which he gave an excellent account of heliocentricity, to Pope Paul III. Copernicus entrusted this work to Andreas Osiander, a Lutheran clergyman who knew that Protestant reaction to it would be negative, since Martin Luther seemed to have condemned the new theory, and, as a result, the book would be condemned. Osiander wrote a preface to the book, in which heliocentrism was presented only as a theory that would account for the movements of the planets more simply than geocentrism did—something Copernicus did not intend.
“We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness.”
Galileo had these same rights, from God. The church trampled upon them.