Yes wrong. GR says that they are physically and observationally indistinguishable. That is far different from your claim that saying that "no one point of reference is preferable over any other" as you did.
This is why Hoyle said, "Today we cannot say that the Copernican theory is ‘right’ and the Ptolemaic theory ‘wrong’ in any meaningful physical sense."
I gave you this quote already. Did you not understand it? You're back to claiming the exact thing that was already refuted.
"We have other observations that confirm the Earth revolves around the Sun."
No you don't. Ellis said, "For instance, I can construct you a spherically symmetrical universe with Earth at its center, and you cannot disprove it based on observations."
I gave you this quote already. Did you not understand it? You're back to claiming the exact thing that was already refuted.
"We couldn't have sent probes to Mars and the outlying planets if heliocentrism was incorrect."
Ernst Mach proved that idea wrong way back in the 19th century. Just who are you listening to? Surely you aren't thinking these things up all by yourself, are you?
Two ways of stating the same concept. If all are indistinguishable then no one is preferable over another.
But that's just GR musings. Sorry, but geocentrism violates the laws of physics. A more massive object does not orbit around a less massive object, look up conservation of momentum. The Earth would have to be by far the most massive object in the solar system, and it simply isn't. Plus I love the tortured explanations for the outer planets that would be going faster than light under the geocentric system.
And just because it's part of a theory doesn't mean it can actually happen. Archimedes rightly said he could move the Earth with a lever and a place to stand to describe general concepts, but that doesn't mean somebody's doing that, or that it's ever even going to happen in a practical sense. Sometimes cool theories run up against plain old reality.