It has been argued that the Pope wanted Galileo to PROVE his belief, which he couldn’t at the time, so it was the Pope who was being more scientific. The long and comprehensive Wikipedia article “Galileo affair”, shows that the issue is not clear cut. Also, if Galileo believed that the sun was the center of the world, then he was wrong - we now know that it’s not even at the center of our galaxy.
I will read your source, as I am not aware of such a documented challenge by the Pope and it would be out of character for the Church, which was not on the habit of inviting open debate on dogma, and in fact the Church had previously promoted Ptolemy’s preposterous “epicycle” excuse for Mars’ retrograde action in desperate support of a geocentric theory they must have suspected was false, but necessary to uphold dogma. Galileo had observed Jupiter and published illustrations of the motions of its moons and remarked on how this support Copernicus’s theory. This is what got him in hot water.