It isn't just what Lester says, but the way Kirk generally agrees with her that gives credence to her claims.
I'm watching my shiny new TOS blu rays, and will watch this episode carefully when I come to it, to see just how clear or vague it is that women really can't be starship captains.
I would point out there's a big difference between a woman sitting in the captain's chair commanding temporarily as first officer and actually being captain.
I remember in a thread in the Lit subforum someone said there's a book that says there was a 100 or so year period where women were banned from being starship captains. Which doesn't prevent a woman from holding the rank of captain while working a different job besides leading a starship.
But then there are books like Vanguard that contradict the sexist ban by having female captains anyways.
I never liked that it was suggested that women couldn't be starship captains, but once that was in place, I'd be curious to see a story that explored the issue, why it happened in the first place, and the resolution being that the ban was lifted and a worthy female officer be promoted to starship captain.
I think there's wiggle room with the Enterprise era that there were female starship captains then, and the ban began somewhere between there and TOS era.
It is a good point to remember TOS was a product of it's era, and it's prejudices. I do like when I read a TOS era book that does things the way I think they should've been done, with stronger female characters with authority.
In a related note, have any of the novels had gay characters in TOS? Vanguard in TOS era certainly has, but what about TOS novels? I know there have been in ENT, TNG, DS9 and Voyager novels. As a gay man I really appreciate finally seeing gays in those stories, and I think that gives me an understanding of how women are written in Star Trek is important.