Non euclidean space time. Photons are subject to gravity interaction just as light is bent (changes direction slightly) passing by a star. Neutrino aren't hence less distance (from a euclidean space time POV) to travel means they get from A to B just a little more quickly.
Nice idea. Could this be verified by math?
If you assume speed of light is constant for both neutrinos and photons, and you know the amount of gravity and straight line distance traveled, I think it would be possible to calculate the travel times for the particles on the curved path (photons) and the straight line path (neutrinos), and compare this mathematical model with the observed results.