It is not as if Macdonald and Whigham were silent on the issue. They both described the concept of the Biarritz Hole, and in their descriptions the actual green is BEYOND the swale, ditch, trench, valley, or whatever you want to call it. The front plateau/approach/ hog-back had to be negotiated by the golfer looking to run the ball through the swale and onto the actual green.
As for the question posed in the opening post, originally a "Double Plateau" was a green concept, whereas a "Biarritz" was a concept for a approx. 215-230 yard golf hole with a swale or ditch before the green.
They were not the same thing, and even when a swale ran horizontally across the middle of the green, it was not necessarily a Biarritz.. Sleepy Hollow originally had two "double plateau" greens, and one of these had the swale running across it horizontally like we think of as a "biarritz" green. But it wasn't a long par three, and wasn't a Biarritz, and it wasn't called a Biarritz, or confused with a "Biarritz." If fact, in addition to these two holes Sleepy Hollow also had a "Biarritz" hole which was a long par three, but that hole didn't have much of what we think if as the Biarritz type swale.
When trying to understand CBM's various concepts, I like to keep in mind his creations at Lido, because there there he had more of a free hand to create what he wanted rather than being guided by the contours as they existed. Here is an image of the 1915 plasticine model of his Biarritz at the Lido.
Notice that the first plateau is not a green.
When writing of the Biarritz, Macdonald referred to the first plateau as a "sharp hog-back" which was follows by a 30 yard ditch, valley, or swale. The "hog-back" was to intended to deflect balls not hit true. Some of these even had two ridges to further deflect offline or poorly struck shots.
As for Yale, if the hole was meant to be a "Biarritz Hole" according to CBM's original conception of the hole, then the first plateau would not have been intended to be pinned. Thus the early descriptions of the hole.
It is possible that as the concept developed that CBM/Raynor (and/or or their clients) decided that pinning the front portion was a good idea (like apparently at Shoreacres,) but if so then this wold have been moving away from the original concept.