It’s not really an important difference; the future and past light cones stay the same but assignment of time coordinates to anything outside them is relative. If it is going faster than light in some reference frames, then in others it will be going faster than light plus backward in time. Of course, a neutrino going through a bar would still have to turn around somehow to get back to the bar’s past.
Also, neutrinos don’t go faster than light in vacuum and in fact are expected to go slower than it, but that’s probably beside the point.
