Regarding that 5 sigma, I remember a joke (here from Wikipedia):
“An astronomer, a physicist and a mathematician are on a train in Scotland. The astronomer looks out of the window, sees a black sheep standing in a field, and remarks, "How odd. All the sheep in Scotland are black!" "No, no, no!" says the physicist. "Only some Scottish sheep are black." The mathematician rolls his eyes at his companions' muddled thinking and says, "In Scotland, there is at least one sheep, at least one side of which appears to be black from here some of the time.”
Of course the joke is too simplified to the point of being mostly false, but the reason I’ve remembered it was that as I’ve read “we can safely conclude that merging black holes do not have a strong, high-energy electromagnetic counterpart” the first I’ve thought was “based just on the observations, they at least don’t always have a strong, high-energy electromagnetic counterpart.”
Of course, if the observed information matches the calculated models, then we can be even more sure than what just the observations alone would say. So were there any reasonable models at all that were able to include the alleged electromagnetic bursts?