Either this is a very biased article, or the interviewed physicists are being extremely polite. The odds of finding new phenomena aren't bad, happens all the time in physics, but of overturning Einsteinian physics? Not very likely, in my opinion.
CERN's reputation for quality research is well deserved, so it wouldn't surprise me at all if the results were replicated, but I'm expecting an eventual explanation consistent with Einstein. This has the same feel as that discovery a decade or so ago of light packets that could arrive before they departed.
Also, given that Fermilab is scheduled to discontinue operation at the end of this year, they might not have sufficient time to do the necessary setup work to their neutrino facility, and experimenters currently on the schedule through the year's end will fight hard to maintain their place.
--Percy