As an example of such a historical myth that we all learned, there is the story that in his confrontation with Cardinal Bellarmine in 1632, Galileo had all the evidence on his side, won the intellectual argument by the weight of that evidence, and was defeated only by the ignorant prejudices the trial judges. However, historical studies have also advanced as more detailed information was obtained and reflected upon.
The actual situation was much more nuanced. The version of Copernican theory defended by Galileo assumed 1. a very small solar system, the size of which should clearly be seen by measurements of planetary parallax and 2. circular orbits, not elliptical (although Galileo knew of the work of Kepler, but declined to incorporate it). Both Copernicus and Galileo had attempted to measure parallax in the solar system, and failed to get a result > 0. (It was only measured by Bessell in 1838.) Furthermore, because it used circles for orbits, the Copernican model was actually less accurate than the old Ptolemaic epicycle system of approximations. In addition, Galileo predicted only a single tide/day, not the actual two.
On the other hand his unambiguous observation of Venus in all four phases in 1610 definitely ruled out the Aristotelian model of heavens, since in this model the sphere of the sun was always beyond the sphere of Venus, although the Tychonic, Capellan and Extended Capellan models were still possible, each either with or without a daily rotating Earth. These latter models had the virtue of explaining the phases of Venus without the vice of the 'refutation' of full Copernican heliocentrism’s prediction of stellar parallax. From Wikipedia's article on Galileo, confirmed by Weinberg.
Conclusion: on the basis of the evidence available to them, the Church had a pretty strong case on the evidence against Copernican heliocentrism, arguably stronger than Galileo. Furthermore, on the basis of contemporary documents and doctrines going back to Augustine and the 4th century, if the church had seen conclusive proof in favor of the Copernican system, it was already formally committed to changing its interpretation. The Church, being engaged in a power struggle during the reformation, would likely have followed conclusive evidence had it been presented.
Refs: see the historically accurate and nuanced video at http://online.itp.ucsb.edu/online/colloq/tutino1/rm/qt.html, for slides see http://online.itp.ucsb.edu/online/colloq/tutino1/, book at Google. This is not an obscure, idiosyncratic view of the Galileo affair, but rather the generally accepted view of knowledgeable scholars.
What other famous oversimplified or false myths of this sort do you know and can document and or reference corrections to?