If they are being misrepresented then it is incumbent on them to clarify what they mean.
I suspect that the following is the case. When it comes to waves of light or fundamental particles (which can act like waves) there exist more than one kind of velocity. There exist the group velocity of a wave/particle. There also exist the phase velocity of the wave/particle. Particles and waves in real life being and end, so do particles. These groups of particles travel at the group velocity. Then individual waves in the group will travel faster and slower than this group velocity.
On human scale velocities and lengths (slower than light and bigger than atoms) these two velocities are equal. They may have measured a much higher phase velocity than c. That is common and I would hope people so decorated and employed at CERN would know this. It is possible that they have simply confused the phase velocity which can be slower or faster than c with the group velocity which according to Einstein must always be equal to or less than c.
Does a group velocity greater than c not mean Einstein was wrong? NO!
Special relativity's postulate of the constancy of the speed of light is really a postulate about the constancy of quantities that are invariant under a type of transformation which is only valid in an unaccelerated reference frame.
From the outset Einstein limited the applicability of Special Relativity to those unaccelerated , inertial reference frames. When Einstein expanded on this with his General Theory of Relativity he restricts Special Relativity even more. In section four of "The foundation of the General Theory of Relativity"
For infinitely small four-dimensional regions the theory of relativity in the restricted sense is appropriate, if the coordinates are suitably chosen. - A. Einstein
"infinitely small four-dimensional regions", meaning that special relativity is only exactly correct on the scale of say particles colliding. On larger scales such as those used in the CERN experiment Special Relativity is not exact, and was never proposed to be exact. In their experiment considerations of General Relativity would come into play. Unless they made a really BIG mistake as told above, then what they may have done is observe some kind of an effect akin to gravitational lensing. The neutrino's mass interacting with the gravitational fields they moved through in such a way that their path to the detector was effectively shorter than the path followed by light. Thus the light would always be faster, but following a longer path through space time could still arrive latter. (Don't quote me on that, I'm just thinking on the fly WTH could explain this result within the accepted frameworks of physics.)
TL;dr There are two kinds of velocity at play in an experiment like the one reported by CERN. The velocity of a single wave/particle, and the velocity of the group. They may have confused group and phase velocities and reached the wrong result. It is possible they have not correctly explained this to the reporters and ended up being misrepresented. An outside result is that they, like a depressingly high number of well educated professional physicist, do not know enough about General Relativity to know that Special Relativity is only valid in "infinitely small regions" and that on a longer scale General Relativity can express itself in surprising ways.
Update: After having read their paper I can only see two ways that this result can be correct, and hundreds of ways they could be incorrect. That is if there was some sort of unexplained dispersion as the neutrino's propogate through the rock. This would mean we have found that they aren't quite as non-interacting as we think they are. The second possibility is that, as I already said the path length of the neutrino's traveling through the gravitational field of the dense rock has been shortened and bent. We know that gravitational fields can do this to light, why not neutrino's?
However let us not strain to find a theoretical explaination for this too readily for as I said there are hundreds of places for them to make a mistake. Errors in calibration can add up and interact in unexpected ways. Such is why in science, we don't consider isolated observations as valid proof one way or the other, only highly suggestive.
Either way things like this show that particle physics is not dead, and the universe still has mysteries to explore.
It seems I was right about them being wrong... the whole thing was caused by a loose wire.
New Theory on that Faster-Than-Light Particle: A Loose Wire