I think the idea was that Khan had so much charisma and just plain sex appeal that she was smitten and ready to jump on him anyway. Certainly not the type of person you'd want working for you, but I took it as more a statement of Khan and his effect on people than a reflection on her.
Also, 60's + hot = dumb. She was pretty, therefore no one was surprised when she decided to go with him.
The exchange which brought it about is one of my favorite TOS moments. Ricardo brought real acting chops. He wants her, she's waffling and says something annoying and Khan says "Then go!" and in about 1/100 of a second you see on his face "Wait... shit... must bang..." and he quickly adds "...or stay. But do it because it is what you want to do." Ah, nice save. Turn it around, give her the option, but make her commit to it. If it's her choice, his conscience is clear. She says she wants to stay, so Khan pushes even more, acts annoyed and says "You must now ask permission to stay." And it works. She begs him to let her stay. His is superior.