Regan claims that if you consult the computer just three times during a game, he will catch you after three games. If you consult just once, it gets a lot harder.
He seems to define "consult" as "receive a specific move from the engine". GMs have stated that they could throw a game simply by being alerted that a good move existed. I doubt that would ever show up on a statistical analysis of moves. It would at the very least require an analysis correlating think time, move, and depth of analysis required to correctly analyze the current position. You'd have to say "hey wait player doesn't usually notice there's some X depth analysis opportunity and actually take it." And that doesn't seem to be the analysis which happened here by a long shot.