If we take for example the Deep Sea Alarm which was presented as a Diving Watch, in 1959...
It came without a turning bezel...which is a bit special for a Diving watch.
So, it is part of the JLC History, don't you think?
So, the reason of th utility is a bit limited.
Then, not seeing it in the flesh, but only in the catalogue is not an evidence that the watch didn't exist.
It may have also existed in a few pieces.
That's part of the JLC Mystery...
Well, I will have to check my eyes, as I still see empty dots on the scans I have.

Best, my friend.
Nicolas