Intresting trivia: heliocentrism didn't show "shining brightly as to be next to irrefutable" - it was a fringe idea that could not be confirmed through observation at the time, required some pretty wild (for the time) assumptions - such as stars being very, very far away, to explain why there's no visible parallax from Earth's movements - and went against existing understanding of physics in general (such as, Earth is very big and heavy and bulky, so it's not obvious how could it be moving in circles very fast). Also, IIRC, the predictions made by heliocentric model were less accurate than geocentric ones.
It took astronomical observations with early telescopes to provide data points favoring a mixed geo/heliocentric model, and then further observations, work of Kepler and Newton's theory of gravity for heliocentric model to finally start making sense.
This does serve as an example backing TFA's thesis: some accepted theories, like (then) geocentric model, may be just local maxima - theoretical dead ends. A potential better theory will initially look bad in comparison, it needs work to develop past the accepted one.