Why Aren't Young Earth Creationists also Geocentrists?

During a discussion a few years ago, a friend made a statement that really made me think and, I have yet to provide an adequately answer. It went something like this:

Young Earth Creationists (YECs) ardently defend a flat, slavishly literalistic interpretation of Genesis, without regard to language, ancient culture or, most importantly, modern science. Yet, curiously, in their view of the cosmos, they reject the literal view of scripture and rely upon modern science. The bible describes the relative motion of the earth and sun 67 times. In 100% of these, the earth is either said to be fixed, or the sun and stars are said to translate across the heavens. There are none that refer to the earth as moving. Calvin was convinced that geocentrism was biblical. Luther was convinced of the same, as well as St. Augustine. In fact, you will not find one single interpretation of scripture that departed from a geocentric cosmology prior to the Renaissance, when man, observing the heavens, proved that the earth orbited the sun.

What gives the YECs the authority to dismiss 1500 years of exegetical tradition and replace it with a secular scientific understanding of the solar system? Do they have some special insight into the text that Luther, Calvin, and Augustine didn't possess? Have they discovered some hidden passage or exegetical insight that proves their interpretations wrong? No. The only information they have that Christians in the first 1500 years of church history lacked is the discoveries of Copernicus and Galileo. In other words, their only reason for rejecting 1500 years of church history and a literal interpretation of scripture is, (gasp) evidence gained from man's wisdom.

My first response to this statement was that the passages in question were merely figures of speech and not literal. But, when he asked how I knew that without accessing knowledge outside of scripture, he had me.