But, LIGO ran their detectors for 8 years at a lower sensitivity with no detections. Almost as soon as they turned on the upgraded detectors in September 2015, they detected the first event (GW150914) which appeared at a level that would have been undetectable previously. Also, they have made two other detections in the 1.5 years since. My guess is that if these events were due to flawed analysis, then we should have seen something during those first 8 years.
Also, it is not just a correlation that has been observed - it is a correlation that has a specific form, a rising fundamental frequency that happens to in line with what we would expect from merging black holes. I know there's an element of circularity in the argument, but what are the chances of that particular sort of signal arising from a spurious correlation?
Even more I'm-not-a-physicist-y speculation; could the additional correlation be some secondary gravitational wave effect hidden under the main signal, pointing to another aspect of the phenomenon?