​System III was originally called PWB 3.0 and early distributions from AT&T has the covers as PWB 3.0 on it.

The name "System III" was a rebranding.   At the time, AT&T wanted to make a run at the enterprise computer business and marketing types did not think the PWB moniker was a good idea when trying to sell it.

You are correct, the PWB 3.0 took a number things from a lot of different places, including the Columbus guys [who gave use the shmat() and ip stuff, as well a Napierville, Whippany etc.], much less what came from Research.

Research Seventh Edition kernel went out to the operating companies in PWB 2.0, so by the time 3.0 was done, the v7's kernel basis was already established.  It was not generally available outside the Bell System, but some people did have it - probably from the OYOC types who brought it with them for some feature or another.     

Clem