There was one run of a hundred American Watch Co Grade KW16's at SN 125,401 that contained movements with Fogg's stud, but not all one hundred of these movements actually have Fogg's stud. For instance, movement SN 125,412 has a vibrating stud with Fogg's patent marked on the balance cock, whereas movement SN 125,423 does not. Movement SN 125,423 has a Fogg's cam regulator instead, and an appropriate balance cock to go with it. Both balance cocks have assembly numbers underneath matching the ends of their respective movement SNs. It is interesting to note that movement SN 125,423 has a hole drilled in the dial plate at the foot of the balance cock to receive the arbor for a vibrating stud, but the AWCo management apparently changed its mind before the intent was executed. The AWCo Grade KW16 examples with Foggs stud have Breguet overcoil hairsprings and more elaborate exposed stopworks than the AT&Co movements, and the upper pivot hole of the vibrating stud arbor is jewelled, making them 20 jewel watches. I believe all known Fogg's stud movement examples of either the AWCo or the AT&Co grades also have Stratton's patented barrel.
I do not know how many AT&Co grade KW16 movements were equipped with Fogg's stud, but Ethan's estimate seems right.
These vibrators are scarce, both in the 20-size and 16-size. I would have preferred to have acquired an AWCO vibrator, but the AT&Co example I acquired had the twin advantages of being available and having a great 18k Browne & Spaulding case.