Yes, I've TOF's blog posts before. TOF's perspective is one that I've encounter many times before. You mostly find it in some very conservative Catholic circles.
If I was being generous, I would say that TOF was pushing back against the overwrought hagiography that often surrounds Galileo and his confrontation with the Church. It's true that the common story is an over simplified account and there are some persistent myths that have worked their way into the story over the years into in order to make Galileo look more heroic and the Church more villainous than they either actually was. The real story is a bit complicated.
But the Church really did ban heliocentrism and it really did punish Galileo for arguing for it. That's not in question. I feel that TOF's argument otherwise rests on a deliberate misrepresentation.
TOF's argument the Church was actually just smartly waiting for proof before it changed it's doctrines is a bit rich in that Galileo offered proof and was punished for it. Now, Galileo's proof was bad, but that's not why he was punished. If it was, the Inquisitors would have mentioned that and not simply accused him of heresy for arguing that the Sun stood still. Not to mention that this whole idea rests on the bizarre notion that science works best when you silence debate until proof can be provided
Ironically, that whole argument stems from a quote from Robert Bellarmine's letter to Foscarini, where he admits that Galileo has a point about not interpreting scripture in a way that is provably false. In that quote, Bellarmine isn't saying that the Church is waiting for proof, he's saying that while proof would force him to change his mind, he doesn't think such proof is possible so he may as well go ahead and ban Copenicanism anyway. It's real obvious if you read the very next sentence that TOF for some reason doesn't quote:
> I add that the one who wrote, "The sun also ariseth, and the sun goeth down, and hasteth to his place where he arose," was Solomon. who not only spoke inspired by God, but was a man above all others wise and learned in the human sciences and in the knowledge of created things; he received all this wisdom from God; therefore it is not likely that he was affirming something that was contrary to truth already demonstrated or capable of being demonstrated.
In other words, he doesn't believe that Galileo or anybody else will be able to find proof that the sun stays still because that would contradict what he already believes based on his reading of the Bible!
So no, TOF is misrepresenting the stance of the Church in 1616. A lot of people repeat this because it looks like a clever debunking of a common myth, but it's actually more of bunking in that he inserts a lot of detail in order to disguise some blatant misrepresentation.