Another thought regarding Bethpage Green #15; the holes on the first nine play down the hill and away from the clubhouse, going up and down slight elevation changes in the small hills across Round Swamp Road.
There is a medium-height hill that plays a large part in the architecture of the second nine; The second nine skirts this hill for several holes, which roughly divides it (Green Course) from the Black Course.
With basically flat, uninteresting terrain at the bottom of the hill, I wonder if Emmet routed some holes around the hill, and others with tees high up on the hill, in a means to create some interest with the golf holes.
After the 14th hole, which plays slightly uphill to the foot of the larger hill, and having to place the 15th hole, I could see the merit behind placing the tees high up on the hill, if in fact this hole was Emmet; it creates a golf hole and shot requirement different than the other par threes on the course.
3 is very much uphill
6 is slightly uphill
11 is across flat ground
15 is markedly downhill
For a point of reference, 15 is located just through the woods from the 4th hole of the Black Course, and play on Black No. 4 can be seen from 15 tee and green.
Upon thinking about this more recently, I think the par three holes may have been "goofy" if they were all in the same direction (e.g. downhill, drop shot holes, holes across a pond, etc.)
Digging a pond does not always create interest in a golf hole.