Everything goes around everything else, unless you want to bring back the aether. So they are both right - there are no special points except the one you choose as your FoR, you can choose earth-centric, heliocentric, pluto-centric, galactic-centre-centric, local-cluster-centric - none of them are wrong.
Except that the center of mass of Solar System lies within or very close to the Sun, so in most practical reference frames it looks pretty much spot on heliocentric. OTOH the only reasonable frame producing geocentric view is the Earth.
You can do the calculations from a different point, CoM makes things easier. It's only mathematically simple, not really objectively special except within a chosen context.
