Yeah that's what it's saying. But it's not saying we get updates as to where the sun is instantly due to FTL gravity. It's saying objects rotate around a projection. If the linear path of the sun were to change, those changes would take a while to get to us to update our path, but also due to how that can't "just happen", things don't end up getting messed up.
But isn't sun rotating around galaxy center? So the velocity of sun isn't line, but an orbit, so it isn't constant (it's always changing direction), and we (Earth) do orbit the place that sun would be if not for the acceleration of sun caused by combined gravity of galaxy?
