You can toss all those stats the PGA tour creates out the window when you play firm fast conditions with 30-40 mph winds. Can you keep it below the wind? Do you know how to play the ground game, the bump and run? Do you know how to contact the ball on soil that feels like concrete, not taking a divot the size of a pelt? Does your ball have a high or low spin rate?
Links golf is unlike anything we play in the States, other than Bandon Dunes Golf Resort and a handful of other courses (most notably on east Long Island), and analyzing the stats is meaningless compared to analyzing who knows how to play links golf.
For you and Patrick to be right, guys who are average or worse at hitting fairways and greens in the U.S., must hit greens under much more trying conditions at the Open Championship. Goes against my instincts, but maybe you are right.
I think you need to supply some actual facts to back up your idea though. Would love to see if guys who hit the most greens and fairways win a lot there. George Pazin showed that Harrington this year was maybe average at hitting greens and fairways. He putted beautifully though. And Rocco shot 69 the first day, while hitting 3 greens. It's hard for me to see how this is an example of a course that especially rewards ball striking, and downplays putting.
I played just one round on a real links course: Portmarnock, in Ireland.
Ball striking on the PGA tour is a combination of driving distance, fairways hit, and GIR. Add the players ranking in each category. Then compare that total with everyone else's. You get ball striking. It shows how many greens and fairways the player hits (with driving distance added in), compared to other players on tour.