What's the point of someone calling themselves independent under a 2 party system?

I just saw this Stossel show about how most Americans consider themselves politically independent, yet we all know that the U.S. is a 2 party system and it will be for a long time to come. With rare exceptions, a Republican or Democrat will always be elected. I think a lot of 'independents' are either predominantly conservative or predominantly liberal, so they will end up voting for a Republican or Democrat despite labeling themselves as independents. What's the point of the independent label other than to say that you don't march in lock-step with the party you're going to end up voting for anyway? a href="http://www.hulu.com/watch/257266/stossel-thu-jul-23-2011#s-p1-so-i0" rel="nofollow"http://www.hulu.com/watch/257266/stossel…/a