None of the Lady CEOs or GMs that I've seen are like that...(and I know/have worked for and with a number of them)...in fact they realize they have to up their game to compete in a man's world, and they do....
Here's the reality. Even if the CEOs and GMs you've known didn't play both sides of the fence, the fact that it's open to them still provides a buffer of sorts. A guy loses his position at anything, he's more apt than a female to wind up on skid row. Even if women don't play both sides of the fence, they fact that it's available is itself an advantage whether they use it or not. Another advantage they refuse to admit they have.
TJ