Didn't TMoST also establish such widely-accepted bits of backstory as McCoy going through a bad divorce, Spock being the first Vulcan in Starfleet, and Kirk joining Starfleet at a young age?
McCoy's divorce backstory was suggested by DeForest Kelley and worked into the second-season writers' bible by D.C. Fontana. TMoST did publicize the idea, though; its chapter on McCoy's past is practically a paraphrase of his bio page in the bible. It did, however, establish that Kirk entered the "Space Service" at 17, the youngest age allowed, and that he was the youngest "Starship Command Captain" ever (which I take to mean the captain of a capital ship like the Enterprise rather than a smaller ship like the destroyer-equivalent ship he commanded previously).
But TMoST did not claim that Spock was the first Vulcan in Starfleet. It explicitly does refer to other "Vulcans in the Space Service" -- naturally, since it was written after "The Immunity Syndrome." It says that Spock's decision to join Starfleet went against Sarek's view of Vulcan tradition, and that he's the only Vulcan on the Enterprise. I think the "first Vulcan in Starfleet" myth may have arisen in fandom as a misreading of those statements. I can't figure out where else it might've come from.
How could "Balance of Terror" have established that the Romulans had stolen tech from the Klingons, when the Klingons themselves didn't even exist until "Errand of Mercy," much later in the first season?
I think Marsden meant that, by analogy with the unused idea from BoT, a possible explanation for the use of Klingon designs in TEI might be that the Romulans stole the plans.