You're conflating two seperate issues, I think.
The frist is whether what they did to him was wrong. On this, I don't think it's possible to argue otherwise. What was done was wrong, period, and there's no whitewashing. In this regard, their motives are irrelevent.
The second is whether they were dogmatically comitted to geocentrism. This is a seperate question with a more nuanced answer. The facts, I think, indicate the following: they were not dogmatically committed to it, but they were reluctant to abandon it and would not do it without more evidence.
I know we are in full agreement on the first issue. To what extent do you agree with me about the second?
Yes.
To what extent do you agree with me about the second? [whether they were dogmatically comitted to geocentrism]
It wasn't Church dogma (a core doctrine of the faith), but it was the traditional worldview. It appears that they were rather casual about it earlier (pre Galileo) because the traditional interpretation of scripture had no serious competitor. Copernicus could be ignored, as his was only a mathematical model. Bruno got torched (by Bellarmine, by the way), but he had multiple issues so we won't dwell on him.
I'm not an expert on the history of that period, but I suspect that the Galileo affair was really the first time they took a formal position that deviating from the geocentric view was heresy. (Presumably, heresy can involve scriptural disputes that go beyond rejection of an article of dogma; but you'd have to ask an expert on canon law.) Because geocentricism isn't central to the mission of the Church, it could have been ignored; but they went out of their way to get involved in a purely optional issue. They decided to make the solar system heretical -- a blunder of historic significance. Galileo's martyrdom is a consequence of their foolishness, rather than his crankiness. That's the key to my view.
All they had to do was sit back and ignore the thing, letting science do what science does. But they felt, for what must have seemed good reasons to them at the time, that they had to draw a line in the sand. So they did.