I strongly suspect that this is due to human error (say 95%). A few people in this thread are batting around much higher probability but given that this isn't a bunch of crackpots but are researchers at CERN this seems like overconfidence. (1-10^-8 is really, really confident.) The strongest evidence that this is an error is that it isn't being produced at much faster than the speed of light but only a tiny bit over.

I'm going to now proceed to list some of the 5%. I don't know enough to discuss their likelyhood in detail.

1) Neutrinos oscillating into a tachyonic form. This seems extremely unlikely. I'm not completely sure, but I think this would violate CPT among other things.

2) Neutrinos oscillating into a sterile neutrino that is able to travel along another dimension. We can approximately bound the number of neutrino types by around 6 (this extends from the SN 1987A data and solar neutrino data).

Both 1 and 2 require extremely weird situations where neutrinos have a probability of oscillating into a specific form with an extremely low probability but have a high probability of oscillating away from it. (If the probability to go to this form were high we would have seen it in the solar neutrino deficiency.) These both have the nice part of potentially explaining dark matter also.

3) Photons have mass, and we need to distinguish between the speed of light and c in SR. The actual value of c in SR is slightly higher than what photons generally travel at, so high energy very low mass particles can travel faster than the speed of light but not faster than c. This runs into a lot of problems, such as the fact that a lot of SR can be derived from Maxwell's equations and some reasonable assumptions about conservation, symmetry and reference frames. So the speed of light should be the actual value showing up in SR.

One other thing to note that hasn't gotten a lot of press- if neutrinos regularly do this we should have seen the SN 1987A neutrinos years before the light arrived, rather than just a few hours before. This is evidence against. But this is only weak evidence since the early neutrino detectors were weak enough that this sort of thing could have been conceivably missed. Moreover, the Mont Blanc detector did detect a burst of neutrinos a few hours before SN 1987A before the main burst. This is generally considered to be a statistical fluke. But, nother detectors could potentially have been neutrinos traveling faster than the speed of light. Problem with this: Why would none of the other detectors have also gotten that early burst? Second problem: If this were the case the early SN 1987A neutrinos might be still traveling faster than light but it would be much much slower than the claim here. This claim amounts to neutrinos traveling on the order of 1/10,000 to 1/40,000 of c faster than they should. The Mont Blanc thing would require them traveling faster on the order of a (10^-9)c faster than they should.