You're right, any scientific theory should be open for revision, if enough indications arise to do so. At the moment, for GW, that is not the case.
And the faster-than-light neutrino? yeah I was right on the heels of that one.
The researchers that conducted the experiment used a very strong variant of 'important, IF TRUE'. They challenged the community to find out why they got this result. Since then, there has been a mistake traced in the measuring methods. Turns out, neutrino's didn't move faster than light.
And to elaborate a bit more: If this mistake hadn't been found, and the experiment was stamped 'valid', similar experiments would be conducted around the world. And if they found the same results, only then had general relativity had a problem