Not actually valid. You can only shift non-accelerating reference frames without introducing extra gravity sources or fictitious forces. The reference frame of Earth falling around the Sun, and the Sun falling around the Earth, are not equivalent in the way that a frame moving 1000 km/s relative to another is.
If you’re dealing with general relativity, there’s no way to avoid gravity. You can pick a reference frame where you’re not accelerating at the origin, but if you look at a path epsilon away then it will be accelerating against the tidal forces.