I don't know if there's anything "stupid" about what McGivers does. From the beginning, she bets on the winner - and then proceeds to wrap him around her pinky finger, without sacrificing anything important to her.
It's not as if she acts particularly distressed or disappointed at any point. When Khan acts to her liking, she swoons over him. When Khan acts in a manner she disapproves of, off she goes and instantly betrays him, releasing the next champion from the former one's clutches and then standing back to see events unfold. After which she again picks the winner and gets what she wished: an important position next to an important man, away from the drudgery of Starfleet.
I'd say that's pretty smart all the way.
Timo Saloniemi
Basically, she's a typical female, using what she has to get what she wants, with no loyalty to anything but herself. That's not a bad quality at all, it's what makes our mothers fight for us.