Mashey and crew basically did most of the original group work as part of PWB. If you look at the Sixth Edition sources and the PWB 1.0 stuff, that is one of the places you will find differences. With Seventh Edition (or I believe as part of the UNIX/TS work that Ken picked up), the Mashey group changes went back into the Research stream. With one of the predecessors to 4.2BSD (it may have 4.1A or 4.1B but frankly I have forgotten) Joy introduced the group scheme we all use today.
The Mashey scheme allowed an UID to be assigned to multiple groups, but only use (be in) a single group during the process lifetime. IIRC the RJE system was based on it, but there were some other scripts that the PWB team needed. Check the original PWB docs, there is some explanation of them. FWIW: new group was added to be similar to switch user (su), to change the gid when the setguid bit was not set on the file. The truth is the early group stuff was not used by most admins.
With BSD and use of UNIX for large systems (particularly academic teaching systems), the desire to have some processes be in more than one group and be able to test the group file protections accordingly was desired -- for things like creating a group for each class - where the hand in system was write-only to the class's TA who was also part of the group.
I'm sure it was used in many other ways, but that was certainly one scheme we used at UCB when wnj added them. Again check the 4.2 docs, where the BSD group scheme is explained. This did seem useful and System V picked it up also fairly soon after BSD released it to the world, and fortunately did not change the BSD semantics.