It's possible that
Coach may have made it that way for a short time. The few catalogs I have all show a single strap. Or it's possible there was an earlier version with slightly different details.
EDITED TO ADD:
The one in the above listing is much older than the olive one we talked about before and probably IS a Cashin-era bag, judging by the very old-style Coach tag inside. That style seems to have been discontinued some time before the mid-1970s according to the catalogs I've seen, and then re-introduced around 1984-85. There's no sign of it in the 1976, 1981, 1982 or 1983 catalogs, and it reappears by 1985. The tan one from Azuremerekat also may be Cashin-era, but the olive one had a full stamped creed and serial number and would have to have been from the mid-80s. The two earlier bags seem like they should have had the same length straps.
The questionable strap we talked about a few days ago from azuremerekat was also a LOT shorter - the seller listed it as a 13-inch drop, which no one except a hobbit would ever have have been able to wear cross-body, but the pics in the listing you just mentioned show a much longer strap that
can be worn cross-body. I'd guess the drop on that one to be at least a 17 to 20-inch drop, which would fit with the size(s) available at Coach.
I can't even imagine that style being made with a 13-inch drop strap. Not only would that NOT have been the fashion so many years ago - going back to the 60s and 70s a "Shoulder bag" didn't mean a purse with a short drop that was carried under the arm and close to the body like it does today. It meant a bag with a
very long strap, like what we'd call a Crossbody today, that hung straight down from one shoulder and fell usually from just below the waist to the lower hip. Hanging straight down was much more common than crossbody, which was thought of as more of a military look.
I also can't imagine a double-turnlock bag like that being carried right under the arm like most bags today (what I always think of as "armpit bags", sorry!) since it seems like the back turnlock would be constantly digging right into your ribs. So it's hard to see a double-turnlock bag with a 13-inch drop being practical, especially 30 or 40 years ago.