People seem think think this allows our current theories to be wrong.....
Perhaps there might be small issues with Einstein theories, personally I doubt it, but, to me, I really don't think small fixes to the theory will explain this stuff away.
However, it is not correct to call this a "small improvement." Relativity was a radical change to our understanding of how the universe behaves. In a Newtonian universe, information (including gravitation, electrical attraction, and light) travelled instantaneously. This does not happen in relativity, and nor does it happen in the universe we live in. Einstein did not merely improve upon Newton's work; Einstein proposed a theory which explained the ways in which we do not live in a Newtonian universe. Thomas Kuhn goes into this concept in detail in "The Structure of Scientific Revolutions."
I'd rather call it a paradigm shifting revolutionary idea ;)
I am a physicist (well, I studied as one, before going technology entrepreneur), and have always sat in the "dark matter is bullshit" camp - so my opinion is likely tainted.
I think a far more likely explanation, as this paper could suggest, is that something far more mundane is happening.
For instance, we already understand tidal forces - that bodies can become tidally locked, that there is an inertial frame shear that drags bodies along around a rotating centre of mass, and exchanges energy between an orbiting body and the centre.... So why is it infeasible that galaxies are tidally locked, and the lack of fall-off in radial velocity is down to the gravitational shear from the galactic core being far more intense than we anticipate, causing the behaviour we see. It doesn't require a rewrite of relativity, "just" of galactic evolution.
Either that, or galaxies are sprites, and lazily rendered ones, at that.
Because someone has indubitably already ran the numbers. The tidal force only has a non central, orbit changing influence on spatially extended bodies, and its effects even on objects as large as our solar system are completely negligible, as it doesn't seem to have a measurable effect on the orbits of the planets. The rotation curves are way off, which is a huge chunk of excess angular momentum that no tidal force can conjure. Where would it even come from, the rotational angular momentum of component stars?
As to running the numbers - agreed - but one can get an answer which is correct but incorrect if your premises are incorrect.
At a galactic scale the perturbations are likely tiny, but a tiny force applied over enough time adds up.
Anyway. It's a poor example that's almost certainly wrong but my point was more about how a single incorrect assumption can wreck a model.