I found a very old catalog from 1981 showing the same strap mounting AND the same dog-leash clip as the one on the black bag. I also found another tPF member selling a VERY old Basic Bag that looks like one of the earliest to have a serial number - I think the creeds showing the small "C" with a circle that's the copyright emblem were the first creed stamps used. Take a look at the details on her Basic Bag which is probably from the mid-1970s and which also shows the same clip and shorter leather piece on the sides of the bag where the strap rings are mounted:
http://www.ebay.com/itm/Vintage-COA...277?pt=US_CSA_WH_Handbags&hash=item2ebd960d6d
It looks like a few changes were made over the years, which isn't surprising. Here's a close-up of the clip and mounting from
Coach's 1981 catalog, compare it to the others - oh, and that seller lists the strap drop as 14 inches which would be about a 30-inch overall length, so it would be shorter than the newer versions which had shoulder straps of either 36 or 44 inches. Pics in order are:
1976 with old-style clip, thinner D-rings and shorter strap ring tabs
1981, same as 1976
1982, same as 1976
1986, new style Dog-leash clip, the same style Coach is still using. Thicker D-rings
1989, same as 1986 plus you can just make out the longer leather strap ring tabs
So sometime between 1982 and 1985 the strap mounting design and the dog leash clip style were both changed. Your bag is perfectly genuine although the strap has probably been replaced.