That's right. The truth as I understand it went like this:
- Gene gave a plum co-starring role to one of the women he was cheating on his wife with, Majel, who wasn't very good on screen.
- NBC execs liked the idea of putting a woman in such a prominent spot, but said a better or more charismatic actress would be needed.
- Gene lied to Majel to spare her feelings, saying that NBC wouldn't allow a woman to hold a high rank.
- In order to keep up that pretense, Gene had to nix the idea of a female executive officer. This ended up being very good luck for Leonard Nimoy-- and searingly bad for gender equality in STAR TREK going forward.
- Gene's lie to Majel, which had to be preserved for the sake of their relationship, took on a life of its own, becoming a well-publicized and self-aggrandizing story of Roddenberry fighting the male chauvinist pigs at NBC as much as he could, but just not winning. The actual executives, who had been all in favor of a strong female co-star on STAR TREK, felt slandered by this, but they apparently never tried to make their case publicly. The fan community just wasn't high enough on their radar, I'd guess.