Ed, one reason more greats have won at ANGC is the field. The Masters has a much smaller, limited field. I think under 100 golfers play each year, and a number of them have no prayer of winning. Only around 40 (plus ties) make the cut. This alone makes it more likely that a "great" player will win:guys like Shaun Micheel and Rich Beem don't even tee it up. Put another way, the Masters is easier to win, once you do qualify. There is less competition.
Your British Open stats are skewed as well, I feel. First, they include six victories before 1915, by Harry Vardon. 3 of those came in the 1890's. Leaving aside the question of whether results from that time should count, Vardon only played 3 U.S. Opens. At most he played in one PGA, and I think none. This throws off any comparisons between these championships.
Other reasons we might need to lower your British Open numbers: from the early 1930's till 1960 most of the world's best golfers did not play there. I wonder if it should even be considered a major during that time. If so, take off 3 more victories (Snead, Hogan and Player in 1959). From 1960 until 1980 (and perhaps even later) the British Open field was still questionable. Americans were still the best golfers overall, but few played: only the very best players made the trip. Like at the Masters, this gave a big advantage to the great players who did take part.
Bottom line, the nature of the field explains at least some of the differences. The Masters has weaker, smaller fields than the U.S. Open and PGA. The British Open had weaker fields for many years. Giving a big advantage to the great players who did play. That's my argument, anyway.