Hah this is a really good point. IIRC the Catholic Church was actually OK with using heliocentric mathematical models, just not with interpreting them as factual.

I wonder what really happened. I'm guessing Galileo was one of those vocal people that just can't help poking the bear.

Edit: reading up a bit more it seems Galileo had a bit of a Linus T. streak, with gratuitous insults and ad hominems against authority. Makes me want to read the source documents now :-)

This isn't true, because one frame is an inertial frame and the other is not (i.e. not real).