Well, sure - those are code words. Nobody, man or woman, brags about how "strong and independent" they are unless they are full of self-doubt.
The most intelligent and high-achieving professional woman I know is such a sweetheart you would never guess what she does for a living unless she told you. And most of the women I've known who fit the "Amazon bitch" mold (and there really aren't many) are borderline incompetent, and they try to bully people to cover that up.
I have consistently found that a strange thing for either a man or woman to say. When I probe it, I always confess that I just don't think I have the perspective, detachment, or clarity to evaluate my own emotional/mental strength or independence. This observation & distinction tends to befuddle whoever I am speaking with. Smart folks, I suppose, huh?