It should have been changed by airdate. You know, "get the new theme on by the first episode in November" sort of thing. From what I've been told by those who remember, The Corbomite Maneuver never had the electric violin theme. It was 10th aired, even though it was the 1st regular episode filmed. According to a person who has video cassettes of the early 80's syndication run, only the first 8 episodes had the spacy theme.
Yeah, the series was very serious, grim and with a good amount of scares. I could see kids hiding behind the courch during a few early shows. This was Trek in its base form with "proto Spock" coldness (and pixie smiles), Kirk's self doubts and stuffiness, and lots of time for the supporting players. I actually found Spock to be more interesting in these early episodes. He was cold, repeatedly stated he was deoted to unemotional logic, but still gave out little smiles and amused head tilts. He was truly alien and not a punchline.