Patrick.
Piping Rock was the first so-called "Biarritz" built by CBM and HJW, and it was described as based on a hole at Biarritz (see Whigham description below.)
I think perhaps the evolution was opposite your description. CBM's original "Biarritz" concept was the long par three with a hogback then a 30 yard swale short of a plateaued green. At some later point in time people got confused and thought the hole must have come from the "Chasm" hole which was the most famous hole at Biarritz. Perhaps the "Chasm" concept got folded into the understanding at Yale or elsewhere.
Briefly on the history of the original concept . . .
CBM and Whigham visited Biarritz (with Arnaud Massy) in early 1906 on their tour of great courses in preparation for the creation of NGLA, and CBM mentioned what became known as his Biarritz concept shortly thereafter in a letter printed in a June 20, 1906 NY Sun article about his recent trip abroad:
"The best holes have not been found on the five British championship links alone. . . . The idea for one hole comes from Biarritz. The hole in question is not a good one, but it revealed a fine and original principle that will be incorporated into my selection."
No mention of the famous chasm --the description of the hole as "not very good" would seem an incongruous reference if he was referring to the famous Chasm. While CBM referred to the 12th hole, at that time the Chasm hole at Biarritz was the 3rd hole and was only around 100 yards or less, and flipping the nines doesn't work because of quirks in the layout. And I have never read any description of the famous Chasm Hole that mentioned a hogs-back or a swale, or the method of playing using the ground game. So, as far as I can tell, the original Biarritz concept was based on a different hole at Biarritz, likely one down by the water in the Chambre d'Amore (the 12th on the map.)
CBM expanded on the description later that year in his article on ideal holes in Outing Magazine where he provided a sample listing of 18 holes:
"15. 210 yards. Suggested by 12th Biarritz making sharp hog back in the middle of the course. Stopping thirty yards from the hole bunkered to the right of the green and good low ground to the left of the plateau green."
Again no mention of the famous Chasm. Rather, CBM described a "sharp hog back" in the middle of the course [hole] ending 30 yards short. And the green is a plateau, with a large swale short of the green.
H.J. Whigham repeated this early understanding in 1913 when describing the inspiration for Piping Rock's Biarritz:
"There is a Biarritz hole of about 220 yards which is new to this country and is one of the best one-shot holes in existence. There is a hog's back extending to within thirty yards of the green and a dip between the hog's back and the green."
Again, nothing about a Chasm, and nothing indicating that they were referring to the Chasm Hole (which was quite famous and called "The Chasm") as opposed to a less noteworthy hole at Biarritz.
____________________________
Nigel,
I think you have Patrick's position accurately, but I think he has it slightly backwards. The Biarritz (long par three, hogsback across middle, then a swale for 30 yards short of the green, then plateaued green) came first. If the "chasm" element is indeed an element of the hole concept (which I doubt) it was added later.