This is debunked b.s. as we have long known...
As with any historic fact, there are aspects that will vary according to the reteller, and depending on whose barrow is being pushed. GR's anecdote is immortalized on his LP and was told to live audiences in universities and at conventions for decades. He told a version of the truth that guaranteed him laughs (he kept the Vulcan and married the woman, because he couldn't legally do it the other way) and didn't embarrass his former wife (and Majel) publicly by discussing his marital indiscretions.
The alternative story, that NBC objected only to GR's mistress being cast, is in a book by Justman & Solow that attempts to debunk many GR anecdotes. They had nothing to lose and who knows how acurate their memories were, or what opposing-view memos weren't preserved. I'm sure the truth is both versions, plus something in between. IIRC, Solow eventually married the writer of "Gene Roddenberry: The Last Conversation". What interesting honeymoon arguments they must have had.
Paula reports the version she heard from the horse's mouth. Nothing wrong with that.