@Gnu - That is true for any two-body system, but when you start adding more celestial bodies a justification arises for choosing one reference point over another. For example:
You second quote is true, but now add in the other planets. If you chose the Earth as the origin of the coordinate system, then the sun would indeed revolve around the Earth.....but NOT the other planets. They would appear to have strange, unexplainable loopy orbits. This was in fact the very reason the heliocentric model was discovered, because the orbits of the other planets were unexplainable, unless one posited the sun as the center of the system....then everything made sense.