I am not a physicist, so pardon me for the bad science.
Maybe particles have cores that are non-space (as opposed to space, ie. vacuum).
I do not know how to calculate the number of particles a neutrino need to 'tunnel' through in 700km of solid matter. But let assumes it is N; knowing that the neutrinos 'skipped' 18 meters during this journey, then 18/N meters might give us the diameter of each particle's core. This seems to be able to explain all the observations thus far: SN1987A, CERN-OPERA, numerous past measurements of 'c', and consistent with theory of relativity.
The significant aspect of CERN-OPERA experiment is that we have been measuring 'c' in vacuum and this is the rare occasion we are measuring 'c' in solid matter. It is unsurprising that we get new data. It will be interesting if CERN's scientists can 'point' the neutrino beam at other neutrino detectors on the other side of Earth (ie. distance of 12,000 km - diameter of Earth) . This will give us new sets of data (distance-time pairs) to prove or disprove this and other hypotheses.