the notion of a frame of reference is independent of that of the center of any given orbit. "frame of reference" simply means choosing some origin for your coordinate system¹; although a stationary frame of reference is easier to work with, in practice the convenient frames of reference all track either the sun or the earth.

there is also the question of whether to use an inertial frame, or a rotating one. a properly rotating frame of reference² can have coordinates of locations on the surface of the earth remain fixed; and in these coordinates, the sun would indeed appear to orbit the earth, because the addition of the virtual rotation requires a "fictitious" force³.