It took 26 years to confirm, and that's thanks to having man-made high flux sources. Detection of solar neutrinos had to wait until the 60s. Funnily there was a puzzle with those, as around two thirds of the ones you could expect seemed to not being there (again). This mismatch took another 40 years or so to confirm, so now we know that there are neutrinos indeed and that they show flavour oscillation, that's why if your experiment is looking for a particular leptonic flavour, well you're missing the other two.
So this is not the first time such there must be something there I can't see, yet I can say something about so it all fits together does the job. Hopefully it won't be the last time.
Edit: even if it turns out that dark matter is the best theory, it would still be a conceptual disaster. But so is QM. Nature seems not to care what we find conceptually appealing.