So their statistical model is based on the ASSUMED relative evolutionary relationships.....
No, the phylogeny wasn't merely "assumed". Phylogenies have been around for over a century and are based on diverse data, e.g., comparative anatomy, biogeography, the fossil record, comparative genetics. The point of this paper was to demonstrate the superiority of their phylogenetic model over others, by showing how it correctly identified genetic function at a much higher rate (96%).
So how is this a scientific method again?
They had a hypothesis (our phylogenetic model more accurately reflects evolutionary relationships than others).
They tested this hypothesis by inputing genetic sequences from very diverse organisms into the model.
Had the output been no better than chance (usually less than 25%), they would have concluded that the model was not an accurate representation of evolutionary relationships.
Had the output been better than chance, but worse than the other models, they would have concluded that the model was a worse representation of evolutionary relationships than the others.
But what they got was an output that correctly identified genetic function to a 96% degree of accuracy, far superior to other models, thereby confirming that their model is at least 96% accurate in the way it represents evolutionary relationships.
That's how science works. If you think you have a model that is a better representation of reality, you test that model and see what you get. They did exactly that and got extremely powerful confirmation that their model is very close to reality.
How is this NOT circular reasoning?
Maybe you should explain how you think it is circular, because I have no idea where you got that from.
The model is based on an assumption
As I said, it's not an assumption, but is based on other data.
and when the data is passed through this model, it verifies the assumption. Nothing to it.
That's how science works.
You test your ideas. And that's exactly what these scientists did.