It would be easy to dismiss what Lester says in the episode if it weren't for her scene with Kirk at the beginning and the tag scene with Kirk ("If only...") at the end. Those scenes make it pretty clear (to me) what idea Arthur Singer was trying to convey in his teleplay for "Turnabout Intruder" -- women cannot be Starfleet captains.
Which is not to say that "The Menagerie" doesn't contradict this. It clearly does. "Turnabout Intruder" also says that General Order IV is the only place where the death penalty is still on the books in Starfleet. "The Menagerie" contradicts that, too. Best just to ignore the whole thing and move on.