What Galileo said doesn't contradict the way things look from earth anyway, it just explains the observable movements more exactly.
Well, not just more exactly. The thing is, if you have a Copernican universe, than certain facts, in particular the retrograde motions of the planets, how and when and where they occur, follow naturally from Copernicism. But if you have a Ptolemaic universe, then there are more degrees of freedom, the solar system
could look Copernican, or it could look completely different. It takes a knife-edge balance of the figures to make a Ptolemaic universe look Copernican --- a mere hair's breadth adjustment to a single figure, and it wouldn't.
So, we live in a universe that looks Copernican. To say that it is
really Ptolemaic, we would need to suppose either:
(1) The Ptolemaic universe is a result of natural causes, and the reason it looks Copernican is the result of a coincidence which is literally infinity to one against.
(2) The Ptolemaic universe was made as is by God, who carefully fine-tuned every single one of its parameters so as to make it look like Galileo is right, because he really likes fucking with physicists.
That's an argument that could have been --- and was --- made in Galileo's time. Today, we have an actual theory of gravity, and the parallel argument with respect to that is still stronger. If we're not right, then we're either the victim of an enormous naturalistic coincidence, or of vast supernatural malice.