The ancient Greeks could predict the movements of the heavens. So could many other cultures. Some of these were RE cosmologies, some FE cosmologies. They are not considered veridical simply because they had predictive power.
A few things you're glossing over here:
1. This doesn't invalidate the observations they made. They did a good job of it.
2. The FE cosmologies you speak of are nothing like most FETs today. They had the good sense to recognize that celestial bodies appear to rotate around the earth and not zip around on top of it.
The move from older cosmologies to seeing the world as spinning around, and not the stars, doesn't change the observations they made. They just assumed the wrong thing was spinning.
The move from seeing the planets moving around crazily to orbiting the sun, likewise, didn't change the observations they made. They just had a way to explain those motions.
The move from Newton to Einstein didn't change the observations that Newton made, either. It just helped explain some anomalies that had been observed in the past (Mercury's orbit, if I remember correctly) and some other things that had been observed more recently.
All of these steps built on top of each other because even if the conclusions were imperfect, they were still based on and fit with observations.
The usual FET model with the sun, moon, stars, and planets doing circles above the plane of the earth doesn't meet those requirements. It describes motions that we don't observe. And it's utterly dissimilar to any of the models along the line so far.
So yeah, the "truth" may change about all of this, but not enough that previous, established models suddenly aren't based on observations or are unable to predict anything.
Newton's models require a round earth, and they still work excellently in many applications. Why is that?