I agree - being an independent woman means you
could stand on your own, and that you don't rely solely on another person (or other people in general) for your own happiness. That doesn't mean that you can't acknowledge that another person
does make you happy, but you're not one of those people who falls apart without a partner.
Incidentally, this put me in mind of this dopey flash thingy:
http://www.rathergood.com/independent_woman/ My brother sent me the link a few years ago (before the whole spongemonkey commercial craze) and it still makes me giggle.