SPDP,
I can understand your confusion as the current Fresh Meadows may be the product of Mr. Herbert Allison, but the Fresh Meadows Country Club that hosted the 1932 U.S. Open won by Gene Sarazen was designed by Tilly. Unfortunately it is no more, having been developed into homes, stores, etc...
In the book, The PGA by Herb Graffis, in the chapter titled "28 holes in 100 strokes," we read, "Fresh Meadow was not a great golf course, but it was a tough one. Like nearly all the courses designed by A.W. Tillinghast... The greens I knew from six years practicing on them..." This was written by the winner of that open, Gene Sarazen.
What is of great interest is the next sentence about the greens, "Uniformly flat and unsubtle, you could get down in two on them regardless of the length of your approach putt." For all who doubt that that the greens at Bethpage were not done by Tilly because they have been described this way, it shows that he had created greens of this type before.