Jason,
Not to answer for Bill McBride, but I can't imagine any connection between the number of rounds and the decision to overseed. Tees get overseeded simply because otherwise players would be hitting off bare dirt as the dormant bermuda was "divoted".
I wouldn't think that the rye overseed on a green would reduce damage to the bermuda on a course with heavy traffic, but I'd love to hear the supers comment on this.