For the basic physics answer, look at Minkowski space: you can define when two events shouldn't be able to effect each other at all if nothing travels faster than light (i.e. they're separated by a spacelike interval).

More basically, we know the direction of causality from other factors; so if the neutrinos are emitted at A and interact with something at B, and both events increase entropy, then you either have to say that they traveled faster than light or that they violated the Second Law of Thermodynamics.