I think the word "proud" is there for the detractors. It's hard to dismiss her as a "lefty" when she is a gun enthusiast herself. I heard her husband on NPR not too long ago and he said they've actually shot at a range since her accident. I found it a bit cringe worthy too. But then, many people get hit by cars driven by drunk drivers, recover and then enthusiastically drive cars again. -Bad analogy?
I have no doubt that she is using that line to make her more acceptable to other proud gun lovers. That's the meaning of "political" - things said, not because you believe them, but because you think it will be effective. Even so, I'd like to ask her for a more specific definition. A more appropriate analogy would be to get hit by a drunk driver, recover somewhat, but continue to be a proud, even enthusiastic drinker. Perhaps even a driving drinker.
(Still bad analogy.)