Within relativity, this is true. Any point can be considered center.
They can be predictable in a geocentric system, a heliocentric system or an acentric system.
They do not know whether they are rotating around the earth or if the earth is rotating beneath them. This is a simple matter of relative motion. Your argument is that since they see the earth rotating below them, this proves the earth rotates. Why can't I argue that since I see the stars rotating around me, this proves the stars are rotating? I won't, because both observations have two possible answers (at least). First the earth is stationary and the stars rotating around it. Second the earth is rotating within the fixed star field. See the issue? That was why my first question was 'what is your fixed reference', which you gave a rational answer, 'there is not one', yet now you are claiming relative references as fixed.
This was Galileo's answer 300-400 years ago. No cosmologist would hang his hat on it. It is quite possible that everywhere besides the center, this occurs, which logically makes sense if there is a center. The idea that there is no center is strictly philosophical, and a "principal" (the Copernican Principle) that cosmologists agree to. There is no firm evidence that it is actually true.
Why? How about because earth is actually at the center, but Jupiter is not? You know that Venus takes something like 247 days for a single rotation right (that is a heck of a long work day)? This does not make sense relative to Jupiter. Why would Venus be different? How about because it is.
Here is a quote from George Ellis:
George Ellis, a famous cosmologist, in Scientific American, "Thinking Globally, Acting Universally", October 1995
People need to be aware that there is a range of models that could explain the observations,” Ellis argues. “For instance, I can construct you a spherically symmetrical universe with Earth at its center, and you cannot disprove it based on observations.” Ellis has published a paper on this. "You can only exclude it on philosophical grounds. In my view there is absolutely nothing wrong in that. What I want to bring into the open is the fact that we are using philosophical criteria in choosing our models. A lot of cosmology tries to hide that.”
Stephen Hawking says:
...all this evidence that the universe looks the same whichever direction we look in might seem to suggest there is something special about our place in the universe. In particular, it might seem that if we observe all other galaxies to be moving away from us, then we must be at the center of the universe.
He does provide and alternative view, though:
There is, however, an alternate explanation: the universe might look the same in every direction as seen from any other galaxy, too. This, as we have seen, was Friedmann’s second assumption. We have no scientific evidence for, or against, this assumption. We believe it only on grounds of modesty: it would be most remarkable if the universe looked the same in every direction around us, but not around other points in the universe.
I have studied this issue for almost 10 years now. I have talked to cosmologists, astronomers, etc. Everything observationally looks like we are in the center. Science objects to it on philosophical grounds, and has spent $billions to try and prove their case, while ignoring the obvious. But of course no establishment would ever do something like that, right?
The current scientific case is unraveling. First they thought the cosmic background was going to prove their case. What did they find? They found that the random noise had an alignment in the universe. Do you know what it is aligned to? The ecliptic! That is not supposed to be there. the CMB is supposed to be completely random. They are so desperate now that they are proposing that there are infinite other universes. Not because there is any evidence there is, nor that they could even produce such evidence, but in order to maintain the Copernican principle AT ANY COST. They are understanding that the earth is in a special place, but are saying, but only in this of infinite other universes. Take a look at this.

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