This is what my brother(physics/math major @ McGill) had to say quickly about it -
Huh...interestingly, I'm taking a break from studying relativity right now. I'm not sure what to think, likely it is a systematic error, or even their statistics could be funky, certainly people will be checking.
Relativity allows for one thing like what we consider the speed of light, one thing that has the property that whatever frame of reference your moving in, you measure it to have the same speed. So right now, we say if you are standing still, or riding on a train, and measure the speed of light, it looks the same in both cases. But we could instead take that speed to be of something else, neutrino's for instance, and have relativity still be consistent.
The reason relativity uses light specifically as the thing which has the same speed in all reference frames is Maxwell's equations, which give the speed of light without reference to any frame of reference, so predict it will be the same in all frames. So if this result is of substance, it could instead be Maxwells equations, and not relativity, that has an issue.
But yeah, overall, my guess is it's an experimental thing. But of course, it would call serious things into question if it isn't.