This definitely refutes the theory that insects are trying to escape towards the light, because, as the article shows, insects don't head directly for the light, but instead move orthogonal to it.
But this doesn't mean they can't use moonlight to help with flying. The theory, as I understand it, is that they use a distant light source -- e.g. the daytime sky -- to maintain altitude. There's no reason they couldn't use the moon to do this too.
Again, they would not be flying towards the moon, they'd be keeping the brightest light to their dorsal side. Since the moon is distant, unlike a lamp, this would result in steady flight.
I'm not sure that it confirms whether they use the moon or not, but it seems like a possibility.