That list has a reference that those of us in the editing field have been griping about for years. We consider the first cut to be the one we do after the completion of shooting. For years, that was the terminology, and I can assure you that we fought long and hard to keep producers from "consulting" with us.
Several years back, the 'suits' decided that editors don't do really do anything creative like producers do and changed the terminology. The old 'editor's cut' is now referred to as the 'editor's first assembly', allowing producers and directors to take credit for the actual 'cutting'. In truth, the 'first cut' they're referring to is actually the producer's first cut which follows the editors cut and the director's cut.
I didn't know that but given the fighting I've seen over credits I am not surprised. I tell the story of the little man who fought like a demon to get an EP credit on a small film based on the fact that two years earlier he had introduced me to a guy who later introduced me to the guys I was going to partner with on the project. He made a real pain in the ass of himself and burned every relationship before he settled for a 'special mention' right before the financing fell through.