I can think of a multitude of greens that are incorporated into their immediate or distant surroundings in a natural way. If you visit Flynn courses you will see the difference in a philosophy that requires taking the time and material to do the tie ins. The tie ins may relate to a feature off in the distance, but it still provides a sense of naturalism. Flynn's greens and surrounds tie in to hillsides and contours sometimes miles off in the distance. This harmony works whether you are looking for it or not. Flynn felt that the natural lines looked better and would require less maintenance over time.
Consider the greens at Cypress Point, Pebble Beach, Maidstone, Friar's Head, Hidden Creek, Pacific Dunes and most greens at Flynn courses such as Shinnecock Hills, Kittansett, Cascades, Huntingdon Valley, Rolling Green, Lancaster, Philadelphia Country, Eagles Mere, Lehigh and especially Pocantico Hills which was meant to be a low-profile estate course.
In my mind, structure by definition constrains creativity. Sometimes creativity can overcome structure but not completely. Rarely do the template greens blend in naturally with the surrounds. You're right, this example is an unusually good one but overwhelmingly the template stands out as unnatural. No doubt they can be fun to play and offer thrilling shots, but not in harmony with surrounds. For the most part, naturalism is subordinated to design concept to an extreme.