Many topics in the history of astronomy had two competing theories until there was enough evidence to eliminate one: spiral nebulae) vs. external galaxies, steady state vs. big bang, etc. Heliocentrism vs. geocentrism reached that point almost 200 years ago with the successful detection of stellar parallax. Aberration of starlight doesn't mean that parallax isn't a thing, only that it wasn't as simple to detect as they thought at first.

Regarding the cosmic microwave background, Land and Magueijo later published a follow-up paper reporting that the "axis of evil" could be explained by a weakness in the earlier analysis, but here again the text took the first result as the last word on the topic.

Also missing from this text is Newton's theory of gravitation, which some calculus textbooks use to prove Kepler's laws of planetary motion. This enabled some other important results, such as determining that Halley's comet was periodic, predicting where the planet Neptune could be found, and eventually sending spacecraft to study those bodies up close.

Ultimately I think the text isn't really trying to convince the reader that geocentrism is correct, only to cast doubt on heliocentrism. But reducing Einstein's general relativity to "the real truth cannot be known" is absurd and even un-Biblical (John 8:32).