The only fact one needs know, and that is that Galileo was _not_ free to walk away, go where he wanted, publish what he would, and call it a theory, a fact, or whatever he pleased.
That is the discussion, not the merits of the theory. The problem was that a religion claimed such authority at all.
And one of the very reasons for the First Amendment denying a "state religion".
Now we have a pope who means to insert himself into American politics AND embrace communism.