Though I loved the adventurous gutsy Nancy Drew books, the very first really strong female characters I came across in my childhood reading were Scarlett O'Hara and Melanie Wilkes; women who showed their strength in different ways.
What does the "strong female character" imply? It gives a special category to women who are nuanced, who are capable of embodying contradictions. But that is the human condition, and to imply that such a woman is not the norm strips all females of their essential humanity
A real person has conflicting feelings all the time and contradicts themselves by accident (as much as we hate to admit it), and it's okay because we're all human. We don't know what we want or how we feel. Or we do. Both is fine. But characters everywhere need to do the same to come alive.
Much like Harry Potter, Katniss is modest because of her desire to keep those whom she loves safe. Her strength and her willingness to sacrifice for the people she loves are what make Katniss, well, Katniss.
If you ask me, falling in love with someone should be seen as a leap of faith rather than a sign of being dependent. Maybe she does go a little weak in the knees, but Bella Swan is far from a weak female character.