I think the argument is that any correlation in the noise must be simply coincidental. In other words, the detection could be explained by chance rather than some true physical phenomenon measured by both detectors.

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.