Basically, it doesn't matter where you set your 0,0,0,0 point.
   [x,y,z,time]

   Want it to be Earth? Go ahead! it's Earth.
   Want it to be the Sun? Go ahead! It's the Sun!

   It's relative. It really doesn't matter what coordinate system
   you use.

   Gravity for example, can ALSO be described perfectly well from a
   perspective of the Earth being at the center of the Solar System
   rather than the Sun. It requires some formula changes, but the
   math will still work out just fine.

   In short, everybody's right.