They believed it and to them this was a fact. Then Galileo came along and showed us otherwise.
Why do you switch from relativism to realism as soon as Galileo enters the picture? You say the sun going round the earth was only true "to them", but you seem to imply that the earth going round the sun is not just true for Galileo, but for all of us. Why's that?
What actually happened was that before Galileo people were mistaken, and he corrected them. To them it was a fact that the sun went roudn the earth, but in reality this was not a fact. Galileo discovered that the earth went round the sun all along
. He did not make this a fact, he discovered that it was a fact.
Facts are common knowledge. Truth is something else, a bit more complicated.
Again, knowledge requires truth. What you mean to say is 'common belief'. You can use the word 'fact' to refer to common belief if it makes you happy, but what word are you going to use to refer to the state of affairs which makes a belief true? I suppose 'state of affairs' would do, but it's not very snappy. 'Truthmaker' is perhaps the best available alternative.
Nobody is suggesting that facts are
truth. We are suggesting that they are the things that are true.