Here's the thing, though. No matter how incomplete our knowledge of science is, it works. We still mark diagrams positive to negative because building a circuit that way works (though for different reasons than we originally thought). Newtonian physics was proven wrong (or at least incomplete) by relativity, but it's still useful to a large degree.
New discoveries aren't going to make us throw away everything we know, they're just going to force us to refine further, to figure out where and why there are exceptions. If neutrinos did move faster than light, that doesn't throw everything we know out the window. It just means that there's one instance where things don't work the way we expect it to. We still know many, many places where it does work the way we expect, because we have years of experiments behind us proving it. The fact that quantum physics counters so many previously held notions didn't make all previously known physics useless. So no, it wouldn't be terrible, awful news if the neutrinos had traveled faster than light. It's not terrible awful news that they didn't, either. It's just another step along the way to understanding the universe.