[TUHS] Did System V Really Prevent 5BSD?

[segaloco via TUHS]

So the prevailing narrative I've heard is that 4.1BSD was so-named at AT&T's demand to avoid confusion with System V.  However, the timeline leads me to question this.  4.1BSD is given as having been issued first June 1981.  Of the Bell lineage, my 4.1 manual also gives June 1981 as a publication date.  5.0 wouldn't release inside AT&T for another year, and System V manuals give 1983 (i.e. post-divestiture) publication dates (although they went to print before, many have Bell logos on the cover still.)

In any case, if System V as a product didn't exist until sometime 1983, how did the fear of confusion with this name prevent the naming of 5BSD in 1981, two years prior?  Was System V as a future trademark already well accepted as a given in 1981?

- Matt G.