I think there is something to this claim for two reasons: First, my dad inadvertently predicted the 1971 Sylmar quake. The night before while we were all seated for dinner, out of the blue, he looked out the window and announced that this was earthquake weather. He never said that before or since. And beyond this, there was a strange calm in the air that night. It is difficult to identify precisely any characteristic, but a strange calm is the best that I can recall. Perhaps it relates to reduced activity for birds and other animals - possibly sensing precursive activity. Or, maybe we can sense pressure changes in advance of some quakes... And there is some evidence that Radon is released in advance of some quakes, so I wonder if this might have an effect on the atmosphere. I distinctly recall that the sun was setting when we sat for dinner, and the sky did look unusual. We all noticed it, and this seemed to be what caught my dad's eye. [edit: Hazy is a word that sort of works for me, but I have thought about this from time to time, and I suspect that there may even be something to the color of the sky... not sure. It has been too long]
Years later I asked him about this. He didn't even remember saying it, but having grown up in earthquake country, he guessed that it was instinctive. He didn't recall anyone telling him about it or what might be the indicators.
