Yup, I do love a good underdog story be it in sports, the movies, or everyday people who seldom get the recognition.
The bad part about the movies though is that the true story is often obscured or changed or even completely different to create a more dramatic story. but in sports, more times than not the action and story unfold right before our eyes. we connect more with the moment and with the people we are experiencing it with as in the case of the Olympics.
I have the same reservations about the movies, as it is made for entertainment, engineered to hit heart strings. However like you say, watching it unfold live is another kind of story.