It has been falsified to any reasonable standard but as a matter of philosophy an objective falsification is impossible.
What the commenter is saying is that you can always add more rules to the geocentric model to force it to be consistent with the new data. The problem is, at some point you might have to account for the fact that your adjustments conflict with other observations either in new data or past results. The sensible thing is to call the theory falsified, but it's never objectively so.
That's why in ideal science you make hypotheses first and then test them. If your predictions don't match the observations we know something is missing. It could be that theory B is more right than theory A or it could be that theory B needs adjustment.
Generally speaking, scientific reasoning is inductive*. We use Ockham's razor as a rule of thumb, but we must remember that it doesn't say "the simpler theory is more likely correct" but rather "given two theories that make identical predictions, we should prefer the one requiring fewer assumptions". But theories don't always make identical predictions.
A good example of when they did was the increasing complexity Ptolomaic astronomy. The geocentric model kept requiring increasingly complicated descriptions of orbital mechanics to fit how planets seemed to "go backwards" in the sky and have all these nested sub patterns or epicycles. Eventually the copernican model better fit observation and it was prohibitive to fit Kepler's work into the Ptolomaic system. This section describes how initially heliocentrism did not offer better predictions than geocentrism but slowly the other facets of geocentrism were undermined. Such issues include the relative locations of Venus and the Sun, the fact that celestial bodies were not "perfect" (showed craters/imperfection as on the moon), and that Jupiter had moons orbiting it.
Nothing about the data can ever objectively show that these equations are entirely "wrong", they were good approximations and then they didn't account for new data. Then they were adjusted and captured the new data. Rinse and repeat.
The heliocentric model was much simpler and straightforward and made better predictions for as yet unobserved data. Most scientists take this as a good indication of it's superiority. Our space probes landing on Mars, the Apollo missions, missions past the Kuiper belt, all these are based, in large part, on the heliocentric model. That they were successful is evidence, but you can always adjust the geocentric model to fit the data. Some flat-earthers spend much effort to this end.
Any theory can be tortured to fit the given data, the question isn't whether it's technically possible, it's whether it's useful.
Don't forget, newtonian physics is just an approximation too! Even once we had the heliocentric model and newtonian gravity we had to explain anomalies in the procession of Mercury. There was a hypothesized inner planet called Vulcan that would have caused this. You can read on it here. We could never find, but then general relatively could explain it without the unobserved planet. Newtonian orbital dynamics are still useful in the right context, but we recognize the limitations.
Regarding your question about the speed of light, there are some interesting relativistic problems in measuring the speed of light. I would point you to the Einstein synchronization convention. Veritasium has an approachable video on this
I tend to like these kinds of philosophical problems but at a certain point they aren't physics. What do we learn by persisting with complicated theories that only barely fit observation? What experiments do they let us do? What do they help us learn? How do they help us progress?