They are measuring the expansion of space (Score 1)

The Michelson–Morley experiment doesn't show that there is no aether , only that we are not moving relatively to it. Particles that have more mass than neutrinos have more inertia to the expansion of space. Since space is expanding uniformly in all directions (like a rising cake), no matter what direction you look, the expansion is the same, the neutrinos get pulled with less resistance through the expanding space than the rest, so they arrive faster.