Paul Feyerabend has a book called Against Method in which he essentially argues that it was the Catholic Church who was following the classical "scientific method" of weighing evidence between theories, and Galileo's hypothesis was rationally judged to be inferior to the existing models. Very fun read.
By Galileo’s era, the Catholic Church was well aware of this scientific truth and actively engaged with astronomy and natural philosophy. The dispute was far more about competing models and the standards of evidence required, not a refusal to accept reason or observation.
Then I can’t help but think: if the author of the article didn’t even understand this, how can the rest of the article be correct if it started from a biased and almost false premise?
That seems pretty unfair. The article is clearly structured to treat the Galileo thing as an example, not a premise. It is supposed to be a familiar case to consider before going into unfamiliar ones. In that sense it clearly still works as an example even if it's false: does it not set you up to think about the general problem, even if it's a fictional anecdote? It's no different than using some observation about Lord of the Rings or Harry Potter as an example before setting into a point. The fact that it's fictional doesn't affect its illustrative merits.