There are two LIGO sites, one in Washington and one in Louisiana. It takes light 10 ms to travel between the two sites.
The entire basis for their claim of detecting gravitational waves is if they see the same signal at both sites occur less than 10 ms apart. A volcanic eruption in Washington, for example, would not show up at the Louisiana site until long after 10 ms had elapsed.
A lightning strike in Colorado however, could potentially show up at both sites within 10 ms. To defeat that, they constantly filter through the data looking for "signatures" of what they would predict two orbiting massive bodies would look like. Which is what happened here, both sites detected the waveform they would expect to see if two black holes were spiraling into each other.
I agree it's somewhat indirect and a little weak, but it's definitely something interesting that happened. But I agree that until they routinely see these signatures from similar sites all over the world and get a lot more data, it is hard to claim they really know for sure what they saw.