GR says that any falling (or orbiting) reference frame is equally valid, locally obeying Newton's laws. So in a precise sense, geocentric and heliocentric reference frames are equally valid. Both can claim to be "actual truth". Of course, a heliocentric reference frame is a lot more useful for studying planetary orbits since it gives rise to simpler equations of state. But that doesn't make the geocentric frame "wrong".
Put differently, would you say a heliocentric reference frame is also "wrong" since the sun is actually orbiting around Sagittarius A*?
Taking your argument to its logical conclusion, one would conclude that the [comoving reference frane](https://en.wikipedia.org/wiki/Comoving_and_proper_distances) is the only "true" one. And at last there is real validity to this claim, since the CMB does pick out a preferred velocity at each point in spacetime. But it is pretty impractical to use comoving coordinates to study problems outside of cosmology.
Ultimately, it stops being a matter of "right" or "wrong" but rather one of picking the right tool for the job you're working on.
Falling is very different from orbiting. Orbiting is accelerating, so requires GR, falling means inertial and only requires SR. Of course, in the larger scheme, all of the frames we care about are orbiting at the very least around the center of the galaxy. But that doesn't make all frames equally useful. It depends on the region of space one is interested in modeling. If it's one wants to model the movement of the planets in the solar system, a heliocentric (or more exactly barycentric) frame is the better one, because it allows for the simplest calculations.
A (free)falling reference frame is also accelerating and also requires GR.
And yes, of course some reference frames make calculations easier for certain areas of study. See my last sentence in the comment you replied to. But that doesn't make one universally "right" and the other "wrong".
Put differently, would you say a heliocentric reference frame is also "wrong" since the sun is actually orbiting around Sagittarius A*?
Taking your argument to its logical conclusion, one would conclude that the [comoving reference frane](https://en.wikipedia.org/wiki/Comoving_and_proper_distances) is the only "true" one. And at last there is real validity to this claim, since the CMB does pick out a preferred velocity at each point in spacetime. But it is pretty impractical to use comoving coordinates to study problems outside of cosmology.
Ultimately, it stops being a matter of "right" or "wrong" but rather one of picking the right tool for the job you're working on.