Admitting that I have not read the whole of the paper, if this were a court of law the proper response would be, "Assumes facts not in evidence".
An initial issue, at least from the Abstract, is that the paper is addressing the situation from within the context of special relativity, which is consistent with a frame of reference that is a flat 4-D Minkowski space time, consistent with special relativity. While even a few years ago we could have assumed that the conclusions drawn from such a perspective were valid, on their own merit. That is not entirely the case today.
It has always been assumed, that general relativity reduces to consistency with Newtonian dynamics locally. This because within the known margins of error Newton's field equations represent a good description of local space. General relativity becomes dominant only in the case of the proximity of "strong" gravitational fields.
The recent results from the GP-B experiment demonstrate that space is curved and dynamic even under gravitational condition traditionally considered to be dominated by Newtonian dynamics. This suggests that instead of general relativity reducing to Newtonian dynamics locally, it is more likely Newton's field equations provide a close approximation of Einstein's field equations, locally.
Since we know know now know that space is locally dynamic, we also know that it is nowhere truly completely Newtonian. Beginning the exploration of a model such as has been put forward within the confines of special relativity is by far an easier task than jumping right into the more complicated field equation and space-time of GR. However, in light of the proofs provided by the GP-B experiment, until the assumptions and conclusions have been verified from the perspective of GR, they can no longer be assumed to be a proof.
This really bothers me personally. However, GP-B has proven that space is locally curved and because of the nature of light we can no longer assume that, in the case of light space and space-time are anywhere anything other than relativistic.
Does this sound like garbage? In some ways it does really bother me, personally. But it does seem that we can no longer treat SR and a flat 4-D Minkowski space time as anything other than a locally close approximation of GR rather than the other way around.
Beyond all this, the paper cited and its conclusions are not consistent with experience.