In my opinion, under either the RET or FET, the Earth can be said to be in a central position in the universe. Without a fixed frame of reference, how are we to say that the earth revolves around the sun, or the sun and the heavenly bodies around the earth? Motion in this sense depends upon the position of the observer, and since we are located on earth as opposed to some random point in the cosmos, this is the best frame of reference as any for our purposes.
With all other arguments aside, the chief response to such a position is usually a reference to Newtonian physics: a body of lesser mass will revolve around the body with greater mass. In an isolated system, a smaller planet will always revolve around the larger one. However, the universe is not an isolated system: it includes all objects, both known and unknown, which displaces the center of mass. It very well could be that the earth is positioned directly in the center of mass of the entire universe, and as such is the unmoving pivot upon which all else turns. Is it? Who knows; we aren't able to step back and view the universe as a whole, to see what our absolute position is. So until we're able to hold the cosmos in the palm of our hand and see just how it is organized in an absolute sense, we have to realize the relativity inherent in our assumptions.